diff --git a/doc/source/timedeltas.rst b/doc/source/timedeltas.rst
index d055c49dc4721..778db17a56b58 100644
--- a/doc/source/timedeltas.rst
+++ b/doc/source/timedeltas.rst
@@ -267,6 +267,14 @@ yields another ``timedelta64[ns]`` dtypes Series.
    td * -1
    td * pd.Series([1, 2, 3, 4])
 
+Rounded division (floor-division) of a ``timedelta64[ns]`` Series by a scalar
+``Timedelta`` gives a series of integers.
+
+.. ipython:: python
+
+   td // pd.Timedelta(days=3, hours=4)
+   pd.Timedelta(days=3, hours=4) // td
+
 Attributes
 ----------
 
diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index 0301bf0a23dd5..d5910fb078ca4 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -294,6 +294,7 @@ Conversion
 - Bug in :meth:`DatetimeIndex.astype` when converting between timezone aware dtypes, and converting from timezone aware to naive (:issue:`18951`)
 - Bug in :class:`FY5253` where ``datetime`` addition and subtraction incremented incorrectly for dates on the year-end but not normalized to midnight (:issue:`18854`)
 - Bug in :class:`DatetimeIndex` where adding or subtracting an array-like of ``DateOffset`` objects either raised (``np.array``, ``pd.Index``) or broadcast incorrectly (``pd.Series``) (:issue:`18849`)
+- Bug in :class:`Series` floor-division where operating on a scalar ``timedelta`` raises an exception (:issue:`18846`)
 
 
 Indexing
diff --git a/pandas/core/ops.py b/pandas/core/ops.py
index 3a7a5e44d5a88..4fde3905c0e65 100644
--- a/pandas/core/ops.py
+++ b/pandas/core/ops.py
@@ -425,7 +425,7 @@ def _validate_timedelta(self, name):
             # 2 timedeltas
             if name not in ('__div__', '__rdiv__', '__truediv__',
                             '__rtruediv__', '__add__', '__radd__', '__sub__',
-                            '__rsub__'):
+                            '__rsub__', '__floordiv__', '__rfloordiv__'):
                 raise TypeError("can only operate on a timedeltas for addition"
                                 ", subtraction, and division, but the operator"
                                 " [{name}] was passed".format(name=name))
@@ -629,7 +629,9 @@ def _offset(lvalues, rvalues):
             # integer gets converted to timedelta in np < 1.6
             if ((self.is_timedelta_lhs and self.is_timedelta_rhs) and
                     not self.is_integer_rhs and not self.is_integer_lhs and
-                    self.name in ('__div__', '__truediv__')):
+                    self.name in ('__div__', '__rdiv__',
+                                  '__truediv__', '__rtruediv__',
+                                  '__floordiv__', '__rfloordiv__')):
                 self.dtype = 'float64'
                 self.fill_value = np.nan
                 lvalues = lvalues.astype(np.float64)
diff --git a/pandas/tests/series/test_operators.py b/pandas/tests/series/test_operators.py
index 433e3cf440cbd..b1d0a749246a7 100644
--- a/pandas/tests/series/test_operators.py
+++ b/pandas/tests/series/test_operators.py
@@ -977,9 +977,7 @@ def test_operators_timedelta64_with_timedelta(self, scalar_td):
 
     @pytest.mark.parametrize('scalar_td', [
         timedelta(minutes=5, seconds=4),
-        pytest.param(Timedelta('5m4s'),
-                     marks=pytest.mark.xfail(reason="Timedelta.__floordiv__ "
-                                                    "bug GH#18846")),
+        Timedelta('5m4s'),
         Timedelta('5m4s').to_timedelta64()])
     def test_operators_timedelta64_with_timedelta_invalid(self, scalar_td):
         td1 = Series([timedelta(minutes=5, seconds=3)] * 3)
@@ -993,15 +991,53 @@ def test_operators_timedelta64_with_timedelta_invalid(self, scalar_td):
             td1 * scalar_td
         with tm.assert_raises_regex(TypeError, pattern):
             scalar_td * td1
-        with tm.assert_raises_regex(TypeError, pattern):
-            td1 // scalar_td
-        with tm.assert_raises_regex(TypeError, pattern):
-            scalar_td // td1
         with tm.assert_raises_regex(TypeError, pattern):
             scalar_td ** td1
         with tm.assert_raises_regex(TypeError, pattern):
             td1 ** scalar_td
 
+    @pytest.mark.parametrize('scalar_td', [
+        timedelta(minutes=5, seconds=4),
+        pytest.param(Timedelta('5m4s'),
+                     marks=pytest.mark.xfail(reason="Timedelta.__floordiv__ "
+                                                    "bug GH#18846")),
+        Timedelta('5m4s').to_timedelta64()])
+    def test_timedelta_rfloordiv(self, scalar_td):
+        # GH#18831
+        td1 = Series([timedelta(minutes=5, seconds=3)] * 3)
+        td1.iloc[2] = np.nan
+        result = scalar_td // td1
+        expected = Series([1, 1, np.nan])
+        tm.assert_series_equal(result, expected)
+
+    @pytest.mark.parametrize('scalar_td', [
+        timedelta(minutes=5, seconds=4),
+        Timedelta('5m4s'),
+        Timedelta('5m4s').to_timedelta64()])
+    def test_timedelta_rfloordiv_explicit(self, scalar_td):
+        # GH#18831
+        td1 = Series([timedelta(minutes=5, seconds=3)] * 3)
+        td1.iloc[2] = np.nan
+
+        # We can test __rfloordiv__ using this syntax,
+        # see `test_timedelta_rfloordiv`
+        result = td1.__rfloordiv__(scalar_td)
+        expected = Series([1, 1, np.nan])
+        tm.assert_series_equal(result, expected)
+
+    @pytest.mark.parametrize('scalar_td', [
+        timedelta(minutes=5, seconds=4),
+        Timedelta('5m4s'),
+        Timedelta('5m4s').to_timedelta64()])
+    def test_timedelta_floordiv(self, scalar_td):
+        # GH#18831
+        td1 = Series([timedelta(minutes=5, seconds=3)] * 3)
+        td1.iloc[2] = np.nan
+
+        result = td1 // scalar_td
+        expected = Series([0, 0, np.nan])
+        tm.assert_series_equal(result, expected)
+
 
 class TestDatetimeSeriesArithmetic(object):
     @pytest.mark.parametrize(