diff --git a/CHANGELOG.md b/CHANGELOG.md
index 65c9ec5f2c2e..328e058bef53 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -39,6 +39,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Hotkeys to switch a label of existing object or to change default label (for objects created with N) (<https://github.com/openvinotoolkit/cvat/pull/3070>)
 - A script to convert some kinds of DICOM files to regular images (<https://github.com/openvinotoolkit/cvat/pull/3095>)
 - Helm chart prototype (<https://github.com/openvinotoolkit/cvat/pull/3102>)
+- Initial implementation of moving tasks between projects (<https://github.com/openvinotoolkit/cvat/pull/3164>)
 
 ### Changed
 
diff --git a/cvat-core/package-lock.json b/cvat-core/package-lock.json
index 2bdc11180320..776e8b2b84e6 100644
--- a/cvat-core/package-lock.json
+++ b/cvat-core/package-lock.json
@@ -1,6 +1,6 @@
 {
   "name": "cvat-core",
-  "version": "3.13.0",
+  "version": "3.12.3",
   "lockfileVersion": 1,
   "requires": true,
   "dependencies": {
diff --git a/cvat-core/package.json b/cvat-core/package.json
index e5e482fde5cb..9ed6e5e7cf03 100644
--- a/cvat-core/package.json
+++ b/cvat-core/package.json
@@ -1,6 +1,6 @@
 {
   "name": "cvat-core",
-  "version": "3.13.0",
+  "version": "3.12.3",
   "description": "Part of Computer Vision Tool which presents an interface for client-side integration",
   "main": "babel.config.js",
   "scripts": {
diff --git a/cvat-core/src/common.js b/cvat-core/src/common.js
index 80134d06f0be..ca30481d7909 100644
--- a/cvat-core/src/common.js
+++ b/cvat-core/src/common.js
@@ -104,6 +104,37 @@
     }
     negativeIDGenerator.start = -1;
 
+    class FieldUpdateTrigger {
+        constructor(initialFields) {
+            const data = { ...initialFields };
+
+            Object.defineProperties(
+                this,
+                Object.freeze({
+                    ...Object.assign(
+                        {},
+                        ...Array.from(Object.keys(data), (key) => ({
+                            [key]: {
+                                get: () => data[key],
+                                set: (value) => {
+                                    data[key] = value;
+                                },
+                                enumerable: true,
+                            },
+                        })),
+                    ),
+                    reset: {
+                        value: () => {
+                            Object.keys(data).forEach((key) => {
+                                data[key] = false;
+                            });
+                        },
+                    },
+                }),
+            );
+        }
+    }
+
     module.exports = {
         isBoolean,
         isInteger,
@@ -114,5 +145,6 @@
         negativeIDGenerator,
         checkExclusiveFields,
         camelToSnake,
+        FieldUpdateTrigger,
     };
 })();
diff --git a/cvat-core/src/server-proxy.js b/cvat-core/src/server-proxy.js
index cf31969a302d..d2b63a9b11b1 100644
--- a/cvat-core/src/server-proxy.js
+++ b/cvat-core/src/server-proxy.js
@@ -1082,7 +1082,9 @@
 
                     const closureId = Date.now();
                     predictAnnotations.latestRequest.id = closureId;
-                    const predicate = () => !predictAnnotations.latestRequest.fetching || predictAnnotations.latestRequest.id !== closureId;
+                    const predicate = () => (
+                        !predictAnnotations.latestRequest.fetching || predictAnnotations.latestRequest.id !== closureId
+                    );
                     if (predictAnnotations.latestRequest.fetching) {
                         waitFor(5, predicate).then(() => {
                             if (predictAnnotations.latestRequest.id !== closureId) {
diff --git a/cvat-core/src/session.js b/cvat-core/src/session.js
index daaee04a21ab..49dcb565f6fe 100644
--- a/cvat-core/src/session.js
+++ b/cvat-core/src/session.js
@@ -16,6 +16,7 @@
     const User = require('./user');
     const Issue = require('./issue');
     const Review = require('./review');
+    const { FieldUpdateTrigger } = require('./common');
 
     function buildDublicatedAPI(prototype) {
         Object.defineProperties(prototype, {
@@ -734,11 +735,11 @@
                 task: undefined,
             };
 
-            let updatedFields = {
+            const updatedFields = new FieldUpdateTrigger({
                 assignee: false,
                 reviewer: false,
                 status: false,
-            };
+            });
 
             for (const property in data) {
                 if (Object.prototype.hasOwnProperty.call(data, property)) {
@@ -865,9 +866,6 @@
                     },
                     __updatedFields: {
                         get: () => updatedFields,
-                        set: (fields) => {
-                            updatedFields = fields;
-                        },
                     },
                 }),
             );
@@ -1040,13 +1038,14 @@
                 dimension: undefined,
             };
 
-            let updatedFields = {
+            const updatedFields = new FieldUpdateTrigger({
                 name: false,
                 assignee: false,
                 bug_tracker: false,
                 subset: false,
                 labels: false,
-            };
+                project_id: false,
+            });
 
             for (const property in data) {
                 if (Object.prototype.hasOwnProperty.call(data, property) && property in initialData) {
@@ -1126,11 +1125,18 @@
                      * @name projectId
                      * @type {integer|null}
                      * @memberof module:API.cvat.classes.Task
-                     * @readonly
                      * @instance
                      */
                     projectId: {
                         get: () => data.project_id,
+                        set: (projectId) => {
+                            if (!Number.isInteger(projectId) || projectId <= 0) {
+                                throw new ArgumentError('Value must be a positive integer');
+                            }
+
+                            updatedFields.project_id = true;
+                            data.project_id = projectId;
+                        },
                     },
                     /**
                      * @name status
@@ -1558,9 +1564,6 @@
                     },
                     __updatedFields: {
                         get: () => updatedFields,
-                        set: (fields) => {
-                            updatedFields = fields;
-                        },
                     },
                 }),
             );
@@ -1721,11 +1724,7 @@
 
             await serverProxy.jobs.save(this.id, jobData);
 
-            this.__updatedFields = {
-                status: false,
-                assignee: false,
-                reviewer: false,
-            };
+            this.__updatedFields.reset();
 
             return this;
         }
@@ -2000,6 +1999,9 @@
                     case 'subset':
                         taskData.subset = this.subset;
                         break;
+                    case 'project_id':
+                        taskData.project_id = this.projectId;
+                        break;
                     case 'labels':
                         taskData.labels = [...this._internalData.labels.map((el) => el.toJSON())];
                         break;
@@ -2011,13 +2013,7 @@
 
             await serverProxy.tasks.saveTask(this.id, taskData);
 
-            this.updatedFields = {
-                assignee: false,
-                name: false,
-                bugTracker: false,
-                subset: false,
-                labels: false,
-            };
+            this.__updatedFields.reset();
 
             return this;
         }
diff --git a/cvat-ui/src/actions/tasks-actions.ts b/cvat-ui/src/actions/tasks-actions.ts
index 3dcf75bcfbc8..cdb993cd1cb0 100644
--- a/cvat-ui/src/actions/tasks-actions.ts
+++ b/cvat-ui/src/actions/tasks-actions.ts
@@ -35,6 +35,7 @@ export enum TasksActionTypes {
     UPDATE_TASK_SUCCESS = 'UPDATE_TASK_SUCCESS',
     UPDATE_TASK_FAILED = 'UPDATE_TASK_FAILED',
     HIDE_EMPTY_TASKS = 'HIDE_EMPTY_TASKS',
+    SWITCH_MOVE_TASK_MODAL_VISIBLE = 'SWITCH_MOVE_TASK_MODAL_VISIBLE',
 }
 
 function getTasks(): AnyAction {
@@ -519,3 +520,46 @@ export function hideEmptyTasks(hideEmpty: boolean): AnyAction {
 
     return action;
 }
+
+export function switchMoveTaskModalVisible(visible: boolean, taskId: number | null = null): AnyAction {
+    const action = {
+        type: TasksActionTypes.SWITCH_MOVE_TASK_MODAL_VISIBLE,
+        payload: {
+            taskId,
+            visible,
+        },
+    };
+
+    return action;
+}
+
+interface LabelMap {
+    label_id: number;
+    new_label_name: string | null;
+    clear_attributes: boolean;
+}
+
+export function moveTaskToProjectAsync(
+    taskInstance: any,
+    projectId: any,
+    labelMap: LabelMap[],
+): ThunkAction<Promise<void>, {}, {}, AnyAction> {
+    return async (dispatch: ActionCreator<Dispatch>): Promise<void> => {
+        dispatch(updateTask());
+        try {
+            // eslint-disable-next-line no-param-reassign
+            taskInstance.labels = labelMap.map((mapper) => {
+                const [label] = taskInstance.labels.filter((_label: any) => mapper.label_id === _label.id);
+                label.name = mapper.new_label_name;
+                return label;
+            });
+            // eslint-disable-next-line no-param-reassign
+            taskInstance.projectId = projectId;
+            await taskInstance.save();
+            const [task] = await cvat.tasks.get({ id: taskInstance.id });
+            dispatch(updateTaskSuccess(task, task.id));
+        } catch (error) {
+            dispatch(updateTaskFailed(error, taskInstance));
+        }
+    };
+}
diff --git a/cvat-ui/src/base.scss b/cvat-ui/src/base.scss
index 9ef0e0ac60c5..4097dbe04692 100644
--- a/cvat-ui/src/base.scss
+++ b/cvat-ui/src/base.scss
@@ -13,6 +13,7 @@ $layout-lg-grid-color: rgba(0, 0, 0, 0.15);
 
 $header-color: #d8d8d8;
 $text-color: #303030;
+$text-color-secondary: rgba(0, 0, 0, 0.45);
 $hover-menu-color: rgba(24, 144, 255, 0.05);
 $completed-progress-color: #61c200;
 $inprogress-progress-color: #1890ff;
diff --git a/cvat-ui/src/components/actions-menu/actions-menu.tsx b/cvat-ui/src/components/actions-menu/actions-menu.tsx
index 52e0f05bcb13..eed1db757567 100644
--- a/cvat-ui/src/components/actions-menu/actions-menu.tsx
+++ b/cvat-ui/src/components/actions-menu/actions-menu.tsx
@@ -33,6 +33,7 @@ export enum Actions {
     EXPORT_TASK_DATASET = 'export_task_dataset',
     DELETE_TASK = 'delete_task',
     RUN_AUTO_ANNOTATION = 'run_auto_annotation',
+    MOVE_TASK_TO_PROJECT = 'move_task_to_project',
     OPEN_BUG_TRACKER = 'open_bug_tracker',
 }
 
@@ -128,6 +129,7 @@ export default function ActionsMenuComponent(props: Props): JSX.Element {
                 Automatic annotation
             </Menu.Item>
             <hr />
+            <Menu.Item key={Actions.MOVE_TASK_TO_PROJECT}>Move to project</Menu.Item>
             <Menu.Item key={Actions.DELETE_TASK}>Delete</Menu.Item>
         </Menu>
     );
diff --git a/cvat-ui/src/components/actions-menu/load-submenu.tsx b/cvat-ui/src/components/actions-menu/load-submenu.tsx
index 347ddbfaa2e2..6f72a7c14cd0 100644
--- a/cvat-ui/src/components/actions-menu/load-submenu.tsx
+++ b/cvat-ui/src/components/actions-menu/load-submenu.tsx
@@ -47,7 +47,12 @@ export default function LoadSubmenu(props: Props): JSX.Element {
                                         return false;
                                     }}
                                 >
-                                    <Button block type='link' disabled={disabled} className='cvat-menu-load-submenu-item-button'>
+                                    <Button
+                                        block
+                                        type='link'
+                                        disabled={disabled}
+                                        className='cvat-menu-load-submenu-item-button'
+                                    >
                                         <UploadOutlined />
                                         <Text>{loader.name}</Text>
                                         {pending && <LoadingOutlined style={{ marginLeft: 10 }} />}
diff --git a/cvat-ui/src/components/annotation-page/attribute-annotation-workspace/attribute-annotation-sidebar/attribute-annotation-sidebar.tsx b/cvat-ui/src/components/annotation-page/attribute-annotation-workspace/attribute-annotation-sidebar/attribute-annotation-sidebar.tsx
index 749a2efdb7a3..155eeeebbf6a 100644
--- a/cvat-ui/src/components/annotation-page/attribute-annotation-workspace/attribute-annotation-sidebar/attribute-annotation-sidebar.tsx
+++ b/cvat-ui/src/components/annotation-page/attribute-annotation-workspace/attribute-annotation-sidebar/attribute-annotation-sidebar.tsx
@@ -2,7 +2,7 @@
 //
 // SPDX-License-Identifier: MIT
 
-import React, { useEffect, useState } from 'react';
+import React, { useState, useEffect } from 'react';
 import { connect } from 'react-redux';
 import { MenuFoldOutlined, MenuUnfoldOutlined } from '@ant-design/icons';
 import { SelectValue } from 'antd/lib/select';
diff --git a/cvat-ui/src/components/create-task-page/project-search-field.tsx b/cvat-ui/src/components/create-task-page/project-search-field.tsx
index 9bab28e2b4fa..4d238cf1c47e 100644
--- a/cvat-ui/src/components/create-task-page/project-search-field.tsx
+++ b/cvat-ui/src/components/create-task-page/project-search-field.tsx
@@ -13,6 +13,7 @@ const core = getCore();
 type Props = {
     value: number | null;
     onSelect: (id: number | null) => void;
+    filter?: (value: Project, index: number, array: Project[]) => unknown
 };
 
 type Project = {
@@ -21,7 +22,7 @@ type Project = {
 };
 
 export default function ProjectSearchField(props: Props): JSX.Element {
-    const { value, onSelect } = props;
+    const { value, filter, onSelect } = props;
     const [searchPhrase, setSearchPhrase] = useState('');
 
     const [projects, setProjects] = useState<Project[]>([]);
@@ -43,8 +44,12 @@ export default function ProjectSearchField(props: Props): JSX.Element {
     const handleFocus = (open: boolean): void => {
         if (!projects.length && open) {
             core.projects.searchNames().then((result: Project[]) => {
-                if (result) {
-                    setProjects(result);
+                let projectsResponse = result;
+                if (typeof filter === 'function') {
+                    projectsResponse = projectsResponse.filter(filter);
+                }
+                if (projectsResponse) {
+                    setProjects(projectsResponse);
                 }
             });
         }
diff --git a/cvat-ui/src/components/move-task-modal/label-mapper-item.tsx b/cvat-ui/src/components/move-task-modal/label-mapper-item.tsx
new file mode 100644
index 000000000000..c4870bf1f750
--- /dev/null
+++ b/cvat-ui/src/components/move-task-modal/label-mapper-item.tsx
@@ -0,0 +1,84 @@
+// Copyright (C) 2021 Intel Corporation
+//
+// SPDX-License-Identifier: MIT
+
+import React from 'react';
+import { Col, Row } from 'antd/lib/grid';
+import Tag from 'antd/lib/tag';
+import Select from 'antd/lib/select';
+import Checkbox from 'antd/lib/checkbox';
+import { ArrowRightOutlined } from '@ant-design/icons';
+import CVATTooltip from 'components/common/cvat-tooltip';
+
+export interface LabelMapperItemValue {
+    labelId: number;
+    newLabelName: string | null;
+    clearAtrributes: boolean;
+}
+
+export interface LabelMapperItemProps {
+    label: any;
+    projectLabels?: any[];
+    value: LabelMapperItemValue;
+    labelMappers: LabelMapperItemValue[];
+    onChange: (value: LabelMapperItemValue) => void;
+}
+
+export default function LabelMapperItem(props: LabelMapperItemProps): JSX.Element {
+    const {
+        label, value, onChange, projectLabels, labelMappers,
+    } = props;
+
+    const labelNames = labelMappers.map((mapper) => mapper.newLabelName).filter((el) => el);
+
+    return (
+        <Row className='cvat-move-task-label-mapper-item' align='middle'>
+            <Col span={6}>
+                {label.name.length > 12 ? (
+                    <CVATTooltip overlay={label.name}>
+                        <Tag color={label.color}>
+                            {`${label.name.slice(0, 12)}...`}
+                        </Tag>
+                    </CVATTooltip>
+                ) : (
+                    <Tag color={label.color}>
+                        {label.name}
+                    </Tag>
+                )}
+                <ArrowRightOutlined />
+            </Col>
+            <Col>
+                <Select
+                    disabled={typeof projectLabels === 'undefined'}
+                    value={value.newLabelName || ''}
+                    onChange={(_value) =>
+                        onChange({
+                            ...value,
+                            newLabelName: _value as string,
+                        })}
+                >
+                    {projectLabels?.filter((_label) => (
+                        !labelNames.includes(_label.name)
+                    )).map((_label) => (
+                        <Select.Option key={_label.id} value={_label.name}>
+                            {_label.name}
+                        </Select.Option>
+                    ))}
+                </Select>
+            </Col>
+            <Col>
+                <Checkbox
+                    disabled
+                    checked={value.clearAtrributes}
+                    onChange={(_value) =>
+                        onChange({
+                            ...value,
+                            clearAtrributes: _value.target.checked,
+                        })}
+                >
+                    Clear attributes
+                </Checkbox>
+            </Col>
+        </Row>
+    );
+}
diff --git a/cvat-ui/src/components/move-task-modal/move-task-modal.tsx b/cvat-ui/src/components/move-task-modal/move-task-modal.tsx
new file mode 100644
index 000000000000..8ccc0f251c93
--- /dev/null
+++ b/cvat-ui/src/components/move-task-modal/move-task-modal.tsx
@@ -0,0 +1,163 @@
+// Copyright (C) 2021 Intel Corporation
+//
+// SPDX-License-Identifier: MIT
+
+import './styles.scss';
+import React, { useState, useEffect } from 'react';
+import { useSelector, useDispatch } from 'react-redux';
+import Modal from 'antd/lib/modal';
+import { Row, Col } from 'antd/lib/grid';
+import Divider from 'antd/lib/divider';
+import notification from 'antd/lib/notification';
+import { QuestionCircleFilled } from '@ant-design/icons';
+
+import ProjectSearch from 'components/create-task-page/project-search-field';
+import CVATTooltip from 'components/common/cvat-tooltip';
+import { CombinedState } from 'reducers/interfaces';
+import { switchMoveTaskModalVisible, moveTaskToProjectAsync } from 'actions/tasks-actions';
+import getCore from 'cvat-core-wrapper';
+import LabelMapperItem, { LabelMapperItemValue } from './label-mapper-item';
+
+const core = getCore();
+
+export default function MoveTaskModal(): JSX.Element {
+    const visible = useSelector((state: CombinedState) => state.tasks.moveTask.modalVisible);
+    const task = useSelector((state: CombinedState) => {
+        const [taskInstance] = state.tasks.current.filter((_task) => _task.instance.id === state.tasks.moveTask.taskId);
+        return taskInstance?.instance;
+    });
+    const taskUpdating = useSelector((state: CombinedState) => state.tasks.updating);
+    const dispatch = useDispatch();
+
+    const [projectId, setProjectId] = useState<number | null>(null);
+    const [project, setProject] = useState<any>(null);
+    const [labelMap, setLabelMap] = useState<{ [key: string]: LabelMapperItemValue }>({});
+
+    const initValues = (): void => {
+        if (task) {
+            const labelValues: { [key: string]: LabelMapperItemValue } = {};
+            task.labels.forEach((label: any) => {
+                labelValues[label.id] = {
+                    labelId: label.id,
+                    newLabelName: null,
+                    clearAtrributes: true,
+                };
+            });
+            setLabelMap(labelValues);
+        }
+    };
+
+    const onCancel = (): void => {
+        dispatch(switchMoveTaskModalVisible(false));
+        initValues();
+        setProject(null);
+        setProjectId(null);
+    };
+
+    const submitMove = async (): Promise<void> => {
+        if (!projectId) {
+            notification.error({
+                message: 'Project not selected',
+            });
+            return;
+        }
+        if (!Object.values(labelMap).every((map) => map.newLabelName !== null)) {
+            notification.error({
+                message: 'Not all labels mapped',
+                description: 'Please choose any action to not mapped labels first',
+            });
+            return;
+        }
+        dispatch(
+            moveTaskToProjectAsync(
+                task,
+                projectId,
+                Object.values(labelMap).map((map) => ({
+                    label_id: map.labelId,
+                    new_label_name: map.newLabelName,
+                    clear_attributes: map.clearAtrributes,
+                })),
+            ),
+        );
+        onCancel();
+    };
+
+    useEffect(() => {
+        if (projectId) {
+            core.projects.get({ id: projectId }).then((_project: any) => {
+                if (projectId) {
+                    setProject(_project[0]);
+                    const { labels } = _project[0];
+                    const labelValues: { [key: string]: LabelMapperItemValue } = {};
+                    Object.entries(labelMap).forEach(([id, label]) => {
+                        const taskLabelName = task.labels.filter(
+                            (_label: any) => (_label.id === label.labelId),
+                        )[0].name;
+                        const [autoNewLabel] = labels.filter((_label: any) => (
+                            _label.name === taskLabelName
+                        ));
+                        labelValues[id] = {
+                            labelId: label.labelId,
+                            newLabelName: autoNewLabel ? autoNewLabel.name : null,
+                            clearAtrributes: true,
+                        };
+                    });
+                    setLabelMap(labelValues);
+                }
+            });
+        } else {
+            setProject(null);
+        }
+    }, [projectId]);
+
+    useEffect(() => {
+        initValues();
+    }, [task?.id]);
+
+    return (
+        <Modal
+            visible={visible}
+            onCancel={onCancel}
+            onOk={submitMove}
+            okButtonProps={{ disabled: taskUpdating }}
+            title={(
+                <span>
+                    {`Move task ${task?.id} to project`}
+                    {/* TODO: replace placeholder */}
+                    <CVATTooltip title='Some moving proccess description here'>
+                        <QuestionCircleFilled className='ant-typography-secondary' />
+                    </CVATTooltip>
+                </span>
+            )}
+            className='cvat-task-move-modal'
+        >
+            <Row align='middle'>
+                <Col>Project:</Col>
+                <Col>
+                    <ProjectSearch
+                        value={projectId}
+                        onSelect={setProjectId}
+                        filter={(_project) => _project.id !== task?.projectId}
+                    />
+                </Col>
+            </Row>
+            <Divider orientation='left'>Label mapping</Divider>
+            {!!Object.keys(labelMap).length && !taskUpdating &&
+                task?.labels.map((label: any) => (
+                    <LabelMapperItem
+                        label={label}
+                        key={label.id}
+                        projectLabels={project?.labels}
+                        value={labelMap[label.id]}
+                        labelMappers={Object.values(labelMap)}
+                        onChange={(value) => {
+                            setLabelMap({
+                                ...labelMap,
+                                [value.labelId]: value,
+                            });
+                        }}
+                    />
+                ))}
+        </Modal>
+    );
+}
diff --git a/cvat-ui/src/components/move-task-modal/styles.scss b/cvat-ui/src/components/move-task-modal/styles.scss
new file mode 100644
index 000000000000..6373a0a800ac
--- /dev/null
+++ b/cvat-ui/src/components/move-task-modal/styles.scss
@@ -0,0 +1,34 @@
+// Copyright (C) 2021 Intel Corporation
+//
+// SPDX-License-Identifier: MIT
+
+@import 'base.scss';
+
+.cvat-task-move-modal > .ant-modal-content {
+    > .ant-modal-body {
+        > div:nth-child(1) {
+            margin-bottom: $grid-unit-size * 2;
+
+            > div:nth-child(1) {
+                padding-right: $grid-unit-size * 2;
+            }
+        }
+    }
+
+    > .ant-modal-header .anticon {
+        margin-left: $grid-unit-size;
+
+        > svg {
+            color: $text-color-secondary;
+        }
+    }
+
+    .ant-select {
+        margin: 0 $grid-unit-size;
+        width: $grid-unit-size * 25;
+    }
+}
+
+.cvat-move-task-label-mapper-item {
+    margin: $grid-unit-size * 2 0;
+}
diff --git a/cvat-ui/src/components/task-page/task-page.tsx b/cvat-ui/src/components/task-page/task-page.tsx
index a6b7fde1a2a0..627dbf9d2504 100644
--- a/cvat-ui/src/components/task-page/task-page.tsx
+++ b/cvat-ui/src/components/task-page/task-page.tsx
@@ -1,4 +1,4 @@
-// Copyright (C) 2020 Intel Corporation
+// Copyright (C) 2020-2021 Intel Corporation
 //
 // SPDX-License-Identifier: MIT
 
@@ -13,6 +13,7 @@ import Result from 'antd/lib/result';
 import DetailsContainer from 'containers/task-page/details';
 import JobListContainer from 'containers/task-page/job-list';
 import ModelRunnerModal from 'components/model-runner-modal/model-runner-dialog';
+import MoveTaskModal from 'components/move-task-modal/move-task-modal';
 import { Task } from 'reducers/interfaces';
 import TopBarComponent from './top-bar';
 
@@ -83,6 +84,7 @@ class TaskPageComponent extends React.PureComponent<Props> {
                     </Col>
                 </Row>
                 <ModelRunnerModal />
+                <MoveTaskModal />
                 {updating && <Spin size='large' className='cvat-spinner' />}
             </>
         );
diff --git a/cvat-ui/src/components/tasks-page/task-list.tsx b/cvat-ui/src/components/tasks-page/task-list.tsx
index 6cd7b96b10f0..3146c60beff4 100644
--- a/cvat-ui/src/components/tasks-page/task-list.tsx
+++ b/cvat-ui/src/components/tasks-page/task-list.tsx
@@ -1,4 +1,4 @@
-// Copyright (C) 2020 Intel Corporation
+// Copyright (C) 2020-2021 Intel Corporation
 //
 // SPDX-License-Identifier: MIT
 
@@ -7,6 +7,7 @@ import { Row, Col } from 'antd/lib/grid';
 import Pagination from 'antd/lib/pagination';
 
 import ModelRunnerModal from 'components/model-runner-modal/model-runner-dialog';
+import MoveTaskModal from 'components/move-task-modal/move-task-modal';
 import TaskItem from 'containers/tasks-page/task-item';
 
 export interface ContentListProps {
@@ -43,6 +44,7 @@ export default function TaskListComponent(props: ContentListProps): JSX.Element
                 </Col>
             </Row>
             <ModelRunnerModal />
+            <MoveTaskModal />
         </>
     );
 }
diff --git a/cvat-ui/src/containers/actions-menu/actions-menu.tsx b/cvat-ui/src/containers/actions-menu/actions-menu.tsx
index acc6a45156e4..f83072bc72cd 100644
--- a/cvat-ui/src/containers/actions-menu/actions-menu.tsx
+++ b/cvat-ui/src/containers/actions-menu/actions-menu.tsx
@@ -4,16 +4,20 @@
 
 import React from 'react';
 import { connect } from 'react-redux';
+// eslint-disable-next-line import/no-extraneous-dependencies
+import { MenuInfo } from 'rc-menu/lib/interface';
 
 import ActionsMenuComponent, { Actions } from 'components/actions-menu/actions-menu';
 import { CombinedState } from 'reducers/interfaces';
 
 import { modelsActions } from 'actions/models-actions';
 import {
-    dumpAnnotationsAsync, loadAnnotationsAsync, exportDatasetAsync, deleteTaskAsync,
+    dumpAnnotationsAsync,
+    loadAnnotationsAsync,
+    exportDatasetAsync,
+    deleteTaskAsync,
+    switchMoveTaskModalVisible,
 } from 'actions/tasks-actions';
-// eslint-disable-next-line import/no-extraneous-dependencies
-import { MenuInfo } from 'rc-menu/lib/interface';
 
 interface OwnProps {
     taskInstance: any;
@@ -33,6 +37,7 @@ interface DispatchToProps {
     exportDataset: (taskInstance: any, exporter: any) => void;
     deleteTask: (taskInstance: any) => void;
     openRunModelWindow: (taskInstance: any) => void;
+    openMoveTaskToProjectWindow: (taskInstance: any) => void;
 }
 
 function mapStateToProps(state: CombinedState, own: OwnProps): StateToProps {
@@ -73,6 +78,9 @@ function mapDispatchToProps(dispatch: any): DispatchToProps {
         openRunModelWindow: (taskInstance: any): void => {
             dispatch(modelsActions.showRunModelDialog(taskInstance));
         },
+        openMoveTaskToProjectWindow: (taskId: number): void => {
+            dispatch(switchMoveTaskModalVisible(true, taskId));
+        },
     };
 }
 
@@ -90,6 +98,7 @@ function ActionsMenuContainer(props: OwnProps & StateToProps & DispatchToProps):
         exportDataset,
         deleteTask,
         openRunModelWindow,
+        openMoveTaskToProjectWindow,
     } = props;
 
     function onClickMenu(params: MenuInfo, file?: File): void {
@@ -119,10 +128,11 @@ function ActionsMenuContainer(props: OwnProps & StateToProps & DispatchToProps):
             if (action === Actions.DELETE_TASK) {
                 deleteTask(taskInstance);
             } else if (action === Actions.OPEN_BUG_TRACKER) {
-                // eslint-disable-next-line
                 window.open(`${taskInstance.bugTracker}`, '_blank');
             } else if (action === Actions.RUN_AUTO_ANNOTATION) {
                 openRunModelWindow(taskInstance);
+            } else if (action === Actions.MOVE_TASK_TO_PROJECT) {
+                openMoveTaskToProjectWindow(taskInstance.id);
             }
         }
     }
diff --git a/cvat-ui/src/containers/annotation-page/top-bar/top-bar.tsx b/cvat-ui/src/containers/annotation-page/top-bar/top-bar.tsx
index d2fcc3808168..351bcc92c0c8 100644
--- a/cvat-ui/src/containers/annotation-page/top-bar/top-bar.tsx
+++ b/cvat-ui/src/containers/annotation-page/top-bar/top-bar.tsx
@@ -8,6 +8,7 @@ import { withRouter } from 'react-router';
 import { RouteComponentProps } from 'react-router-dom';
 import Input from 'antd/lib/input';
 import copy from 'copy-to-clipboard';
+
 import {
     activateObject,
     changeFrameAsync,
diff --git a/cvat-ui/src/reducers/interfaces.ts b/cvat-ui/src/reducers/interfaces.ts
index 2f067ecae8c1..841a0ef612d1 100644
--- a/cvat-ui/src/reducers/interfaces.ts
+++ b/cvat-ui/src/reducers/interfaces.ts
@@ -74,6 +74,10 @@ export interface TasksState {
     fetching: boolean;
     updating: boolean;
     hideEmpty: boolean;
+    moveTask: {
+        modalVisible: boolean;
+        taskId: number | null;
+    };
     gettingQuery: TasksQuery;
     count: number;
     current: Task[];
@@ -245,6 +249,7 @@ export interface NotificationsState {
             exporting: null | ErrorState;
             deleting: null | ErrorState;
             creating: null | ErrorState;
+            moving: null | ErrorState;
         };
         formats: {
             fetching: null | ErrorState;
@@ -310,6 +315,7 @@ export interface NotificationsState {
     messages: {
         tasks: {
             loadingDone: string;
+            movingDone: string;
         };
         models: {
             inferenceDone: string;
diff --git a/cvat-ui/src/reducers/notifications-reducer.ts b/cvat-ui/src/reducers/notifications-reducer.ts
index ae424729391d..e6dce4bffcad 100644
--- a/cvat-ui/src/reducers/notifications-reducer.ts
+++ b/cvat-ui/src/reducers/notifications-reducer.ts
@@ -45,6 +45,7 @@ const defaultState: NotificationsState = {
             exporting: null,
             deleting: null,
             creating: null,
+            moving: null,
         },
         formats: {
             fetching: null,
@@ -110,6 +111,7 @@ const defaultState: NotificationsState = {
     messages: {
         tasks: {
             loadingDone: '',
+            movingDone: '',
         },
         models: {
             inferenceDone: '',
@@ -387,6 +389,24 @@ export default function (state = defaultState, action: AnyAction): Notifications
                 },
             };
         }
+        case TasksActionTypes.MOVE_TASK_TO_PROJECT_FAILED: {
+            const taskID = action.payload.task.id;
+            return {
+                ...state,
+                errors: {
+                    ...state.errors,
+                    tasks: {
+                        ...state.errors.tasks,
+                        moving: {
+                            message:
+                                'Could not move  the' +
+                                `<a href="/tasks/${taskID}" target="_blank">task ${taskID}</a> to a project`,
+                            reason: action.payload.error.toString(),
+                        },
+                    },
+                },
+            };
+        }
         case TasksActionTypes.DUMP_ANNOTATIONS_FAILED: {
             const taskID = action.payload.task.id;
             return {
@@ -440,6 +460,20 @@ export default function (state = defaultState, action: AnyAction): Notifications
                 },
             };
         }
+        case TasksActionTypes.MOVE_TASK_TO_PROJECT_SUCCESS: {
+            const { id: taskId, projectId } = action.payload.task;
+
+            return {
+                ...state,
+                messages: {
+                    ...state.messages,
+                    tasks: {
+                        ...state.messages.tasks,
+                        movingDone: `The task #${taskId} has been successfully moved to the project #${projectId}`,
+                    },
+                },
+            };
+        }
         case ProjectsActionTypes.GET_PROJECTS_FAILED: {
             return {
                 ...state,
diff --git a/cvat-ui/src/reducers/tasks-reducer.ts b/cvat-ui/src/reducers/tasks-reducer.ts
index 2cc8db82e97d..bebb9a628d39 100644
--- a/cvat-ui/src/reducers/tasks-reducer.ts
+++ b/cvat-ui/src/reducers/tasks-reducer.ts
@@ -1,4 +1,4 @@
-// Copyright (C) 2020 Intel Corporation
+// Copyright (C) 2020-2021 Intel Corporation
 //
 // SPDX-License-Identifier: MIT
 
@@ -14,6 +14,10 @@ const defaultState: TasksState = {
     fetching: false,
     updating: false,
     hideEmpty: false,
+    moveTask: {
+        modalVisible: false,
+        taskId: null,
+    },
     count: 0,
     current: [],
     gettingQuery: {
@@ -351,6 +355,16 @@ export default (state: TasksState = defaultState, action: AnyAction): TasksState
                 hideEmpty: action.payload.hideEmpty,
             };
         }
+        case TasksActionTypes.SWITCH_MOVE_TASK_MODAL_VISIBLE: {
+            return {
+                ...state,
+                moveTask: {
+                    ...state.moveTask,
+                    modalVisible: action.payload.visible,
+                    taskId: action.payload.taskId,
+                },
+            };
+        }
         case BoundariesActionTypes.RESET_AFTER_ERROR:
         case AuthActionTypes.LOGOUT_SUCCESS: {
             return { ...defaultState };
diff --git a/cvat/apps/engine/serializers.py b/cvat/apps/engine/serializers.py
index 6e0cacc8dd0d..15739bbafee4 100644
--- a/cvat/apps/engine/serializers.py
+++ b/cvat/apps/engine/serializers.py
@@ -405,17 +405,76 @@ def update(self, instance, validated_data):
             instance.bug_tracker)
         instance.subset = validated_data.get('subset', instance.subset)
         labels = validated_data.get('label_set', [])
-        for label in labels:
-            LabelSerializer.update_instance(label, instance)
+        if instance.project_id is None:
+            for label in labels:
+                LabelSerializer.update_instance(label, instance)
+        validated_project_id = validated_data.get('project_id', None)
+        if validated_project_id is not None and validated_project_id != instance.project_id:
+            project = models.Project.objects.get(id=validated_data.get('project_id', None))
+            if instance.project_id is None:
+                for old_label in instance.label_set.all():
+                    try:
+                        new_label = project.label_set.filter(name=old_label.name).first()
+                    except ValueError:
+                        raise serializers.ValidationError(f'Target project does not have label with name "{old_label.name}"')
+                    old_label.attributespec_set.all().delete()
+                    for model in (models.LabeledTrack, models.LabeledShape, models.LabeledImage):
+                        model.objects.filter(job__segment__task=instance, label=old_label).update(
+                            label=new_label
+                        )
+                instance.label_set.all().delete()
+            else:
+                for old_label in instance.project.label_set.all():
+                    if new_label_for_name := list(filter(lambda x: x.get('id', None) == old_label.id, labels)):
+                        old_label.name = new_label_for_name[0].get('name', old_label.name)
+                    try:
+                        new_label = project.label_set.filter(name=old_label.name).first()
+                    except ValueError:
+                        raise serializers.ValidationError(f'Target project does not have label with name "{old_label.name}"')
+                    for (model, attr, attr_name) in (
+                        (models.LabeledTrack, models.LabeledTrackAttributeVal, 'track'),
+                        (models.LabeledShape, models.LabeledShapeAttributeVal, 'shape'),
+                        (models.LabeledImage, models.LabeledImageAttributeVal, 'image')
+                    ):
+                        attr.objects.filter(**{
+                            f'{attr_name}__job__segment__task': instance,
+                            f'{attr_name}__label': old_label
+                        }).delete()
+                        model.objects.filter(job__segment__task=instance, label=old_label).update(
+                            label=new_label
+                        )
+            instance.project = project
 
         instance.save()
         return instance
 
-    def validate_labels(self, value):
-        label_names = [label['name'] for label in value]
-        if len(label_names) != len(set(label_names)):
-            raise serializers.ValidationError('All label names must be unique for the task')
-        return value
+    def validate(self, attrs):
+        # When moving task labels can be mapped to one, but when not names must be unique
+        if 'project_id' in attrs.keys() and self.instance is not None:
+            project_id = attrs.get('project_id')
+            if project_id is not None and not models.Project.objects.filter(id=project_id).count():
+                raise serializers.ValidationError(f'Cannot find project with ID {project_id}')
+            # Check that all labels can be mapped
+            new_label_names = set()
+            old_labels = self.instance.project.label_set.all() if self.instance.project_id else self.instance.label_set.all()
+            for old_label in old_labels:
+                if len(new_labels := tuple(filter(lambda x: x.get('id') == old_label.id, attrs.get('label_set', [])))):
+                    new_label_names.add(new_labels[0].get('name', old_label.name))
+                else:
+                    new_label_names.add(old_label.name)
+            target_project = models.Project.objects.get(id=project_id)
+            target_project_label_names = set()
+            for label in target_project.label_set.all():
+                target_project_label_names.add(label.name)
+            if not new_label_names.issubset(target_project_label_names):
+                raise serializers.ValidationError('All task or project label names must be mapped to the target project')
+        else:
+            if 'label_set' in attrs.keys():
+                label_names = [label['name'] for label in attrs.get('label_set')]
+                if len(label_names) != len(set(label_names)):
+                    raise serializers.ValidationError('All label names must be unique for the task')
+
+        return attrs
 
 
 class ProjectSearchSerializer(serializers.ModelSerializer):
diff --git a/cvat/apps/engine/tests/test_rest_api.py b/cvat/apps/engine/tests/test_rest_api.py
index c55e70d32151..c99536da13f6 100644
--- a/cvat/apps/engine/tests/test_rest_api.py
+++ b/cvat/apps/engine/tests/test_rest_api.py
@@ -1776,6 +1776,190 @@ def test_api_v1_tasks_delete_label(self):
         }
         self._check_api_v1_task(data)
 
+class TaskMoveAPITestCase(APITestCase):
+
+    def setUp(self):
+        self.client = APIClient()
+
+        self._run_api_v1_job_id_annotation(self.task.segment_set.first().job_set.first().id, self.annotation_data)
+
+    @classmethod
+    def setUpTestData(cls):
+        create_db_users(cls)
+
+        projects = []
+
+        project_data = {
+            "name": "Project for task move 1",
+            "owner": cls.admin,
+            "labels": [{
+                "name": "car"
+            }, {
+                "name": "person"
+            }]
+        }
+        db_project = create_db_project(project_data)
+        projects.append(db_project)
+
+        project_data = {
+            "name": "Project for task move 2",
+            "owner": cls.admin,
+            "labels": [{
+                "name": "car",
+                "attributes": [{
+                    "name": "color",
+                    "mutable": False,
+                    "input_type": AttributeType.SELECT,
+                    "default_value": "white",
+                    "values": ["white", "yellow", "green", "red"]
+                }]
+            }, {
+                "name": "test"
+            }, {
+                "name": "other.label"
+            }]
+        }
+
+        db_project = create_db_project(project_data)
+        projects.append(db_project)
+
+        cls.projects = projects
+
+        task_data = {
+            "name": "Task for moving",
+            "owner": cls.admin,
+            "overlap": 0,
+            "segment_size": 100,
+            "image_quality": 75,
+            "size": 100,
+            "project": None,
+            "labels": [{
+                "name": "car",
+                "attributes": [{
+                    "name": "color",
+                    "mutable": False,
+                    "input_type": AttributeType.SELECT,
+                    "default_value": "white",
+                    "values": ["white", "yellow", "green", "red"]
+                }]
+            }]
+        }
+        db_task = create_db_task(task_data)
+        cls.task = db_task
+
+        cls.annotation_data = {
+            "version": 1,
+            "tags": [
+                {
+                    "frame": 0,
+                    "label_id": cls.task.label_set.first().id,
+                    "group": None,
+                    "source": "manual",
+                    "attributes": []
+                }
+            ],
+            "shapes": [
+                {
+                    "frame": 0,
+                    "label_id": cls.task.label_set.first().id,
+                    "group": None,
+                    "source": "manual",
+                    "attributes": [
+                        {
+                            "spec_id": cls.task.label_set.first().attributespec_set.first().id,
+                            "value": cls.task.label_set.first().attributespec_set.first().values.split('\'')[1]
+                        }
+                    ],
+                    "points": [1.0, 2.1, 100, 300.222],
+                    "type": "rectangle",
+                    "occluded": False
+                }
+            ],
+            "tracks": [
+                {
+                    "frame": 0,
+                    "label_id": cls.task.label_set.first().id,
+                    "group": None,
+                    "source": "manual",
+                    "attributes": [
+                        {
+                            "spec_id": cls.task.label_set.first().attributespec_set.first().id,
+                            "value": cls.task.label_set.first().attributespec_set.first().values.split('\'')[1]
+                        }
+                    ],
+                    "shapes": [
+                        {
+                            "frame": 0,
+                            "attributes": [],
+                            "points": [1.0, 2.1, 100, 300.222],
+                            "type": "rectangle",
+                            "occluded": False,
+                            "outside": False
+                        },
+                        {
+                            "frame": 2,
+                            "attributes": [],
+                            "points": [2.0, 2.1, 100, 300.222],
+                            "type": "rectangle",
+                            "occluded": True,
+                            "outside": True
+                        },
+                    ]
+                }
+            ]
+        }
+
+    def _run_api_v1_tasks_id(self, tid, data):
+        with ForceLogin(self.admin, self.client):
+            response = self.client.patch('/api/v1/tasks/{}'.format(tid),
+                data=data, format="json")
+
+        return response
+
+    def _run_api_v1_job_id_annotation(self, jid, data):
+        with ForceLogin(self.admin, self.client):
+            response = self.client.patch('/api/v1/jobs/{}/annotations?action=create'.format(jid),
+                data=data, format="json")
+
+        return response
+
+    def _check_response(self, response, data):
+        self.assertEqual(response.data["project_id"], data["project_id"])
+
+    def _check_api_v1_tasks(self, tid, data, expected_status=status.HTTP_200_OK):
+        response = self._run_api_v1_tasks_id(tid, data)
+        self.assertEqual(response.status_code, expected_status)
+        if (expected_status == status.HTTP_200_OK):
+            self._check_response(response, data)
+
+    def test_move_task_bad_request(self):
+        # Try to move task without proper label mapping
+        data = {
+            "project_id": self.projects[0].id,
+            "labels": [{
+                "id": self.task.label_set.first().id,
+                "name": "some.other.label"
+            }]
+        }
+        self._check_api_v1_tasks(self.task.id, data, status.HTTP_400_BAD_REQUEST)
+
+    def test_move_task(self):
+        # Try to move single task to the project
+        data = {
+            "project_id": self.projects[0].id
+        }
+        self._check_api_v1_tasks(self.task.id, data)
+
+        # Try to move task from project to the other project
+        data = {
+            "project_id": self.projects[1].id,
+            "labels": [{
+                "id": self.projects[0].label_set.all()[1].id,
+                "name": "test"
+            }]
+        }
+        self._check_api_v1_tasks(self.task.id, data)
+
 class TaskCreateAPITestCase(APITestCase):
     def setUp(self):
         self.client = APIClient()