diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index dfb7a3675fdd5..abfa57dc09334 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -161,6 +161,7 @@ Datetimelike API Changes
 - For :class:`DatetimeIndex` and :class:`TimedeltaIndex` with non-``None`` ``freq`` attribute, addition or subtraction of integer-dtyped array or ``Index`` will return an object of the same class (:issue:`19959`)
 - :class:`DateOffset` objects are now immutable. Attempting to alter one of these will now raise ``AttributeError`` (:issue:`21341`)
 - :class:`PeriodIndex` subtraction of another ``PeriodIndex`` will now return an object-dtype :class:`Index` of :class:`DateOffset` objects instead of raising a ``TypeError`` (:issue:`20049`)
+- :func:`cut` and :func:`qcut` now returns a :class:`DatetimeIndex` or :class:`TimedeltaIndex` bins when the input is datetime or timedelta dtype respectively and ``retbins=True`` (:issue:`19891`)
 
 .. _whatsnew_0240.api.other:
 
diff --git a/pandas/core/reshape/tile.py b/pandas/core/reshape/tile.py
index 8bbf939e110e9..863ebc6354136 100644
--- a/pandas/core/reshape/tile.py
+++ b/pandas/core/reshape/tile.py
@@ -11,6 +11,7 @@
     is_datetime64_dtype,
     is_timedelta64_dtype,
     is_datetime64tz_dtype,
+    is_datetime_or_timedelta_dtype,
     _ensure_int64)
 
 import pandas.core.algorithms as algos
@@ -18,7 +19,7 @@
 from pandas._libs.lib import infer_dtype
 from pandas import (to_timedelta, to_datetime,
                     Categorical, Timestamp, Timedelta,
-                    Series, Interval, IntervalIndex)
+                    Series, Index, Interval, IntervalIndex)
 
 import numpy as np
 
@@ -364,6 +365,8 @@ def _bins_to_cuts(x, bins, right=True, labels=None,
             result = result.astype(np.float64)
             np.putmask(result, na_mask, np.nan)
 
+    bins = _convert_bin_to_datelike_type(bins, dtype)
+
     return result, bins
 
 
@@ -428,6 +431,26 @@ def _convert_bin_to_numeric_type(bins, dtype):
     return bins
 
 
+def _convert_bin_to_datelike_type(bins, dtype):
+    """
+    Convert bins to a DatetimeIndex or TimedeltaIndex if the orginal dtype is
+    datelike
+
+    Parameters
+    ----------
+    bins : list-like of bins
+    dtype : dtype of data
+
+    Returns
+    -------
+    bins : Array-like of bins, DatetimeIndex or TimedeltaIndex if dtype is
+           datelike
+    """
+    if is_datetime64tz_dtype(dtype) or is_datetime_or_timedelta_dtype(dtype):
+        bins = Index(bins.astype(np.int64), dtype=dtype)
+    return bins
+
+
 def _format_labels(bins, precision, right=True,
                    include_lowest=False, dtype=None):
     """ based on the dtype, return our labels """
diff --git a/pandas/tests/reshape/test_tile.py b/pandas/tests/reshape/test_tile.py
index 807fb2530603a..44de3e93d42bf 100644
--- a/pandas/tests/reshape/test_tile.py
+++ b/pandas/tests/reshape/test_tile.py
@@ -7,7 +7,8 @@
 import pandas as pd
 from pandas import (DataFrame, Series, isna, to_datetime, DatetimeIndex, Index,
                     Timestamp, Interval, IntervalIndex, Categorical,
-                    cut, qcut, date_range, NaT, TimedeltaIndex)
+                    cut, qcut, date_range, timedelta_range, NaT,
+                    TimedeltaIndex)
 from pandas.tseries.offsets import Nano, Day
 import pandas.util.testing as tm
 from pandas.api.types import CategoricalDtype as CDT
@@ -605,3 +606,38 @@ def f():
         mask = result.isna()
         tm.assert_numpy_array_equal(
             mask, np.array([False, True, True, True, True]))
+
+    @pytest.mark.parametrize('tz', [None, 'UTC', 'US/Pacific'])
+    def test_datetime_cut_roundtrip(self, tz):
+        # GH 19891
+        s = Series(date_range('20180101', periods=3, tz=tz))
+        result, result_bins = cut(s, 2, retbins=True)
+        expected = cut(s, result_bins)
+        tm.assert_series_equal(result, expected)
+        expected_bins = DatetimeIndex(['2017-12-31 23:57:07.200000',
+                                       '2018-01-02 00:00:00',
+                                       '2018-01-03 00:00:00'])
+        expected_bins = expected_bins.tz_localize(tz)
+        tm.assert_index_equal(result_bins, expected_bins)
+
+    def test_timedelta_cut_roundtrip(self):
+        # GH 19891
+        s = Series(timedelta_range('1day', periods=3))
+        result, result_bins = cut(s, 2, retbins=True)
+        expected = cut(s, result_bins)
+        tm.assert_series_equal(result, expected)
+        expected_bins = TimedeltaIndex(['0 days 23:57:07.200000',
+                                        '2 days 00:00:00',
+                                        '3 days 00:00:00'])
+        tm.assert_index_equal(result_bins, expected_bins)
+
+    @pytest.mark.parametrize('arg, expected_bins', [
+        [timedelta_range('1day', periods=3),
+         TimedeltaIndex(['1 days', '2 days', '3 days'])],
+        [date_range('20180101', periods=3),
+         DatetimeIndex(['2018-01-01', '2018-01-02', '2018-01-03'])]])
+    def test_datelike_qcut_bins(self, arg, expected_bins):
+        # GH 19891
+        s = Series(arg)
+        result, result_bins = qcut(s, 2, retbins=True)
+        tm.assert_index_equal(result_bins, expected_bins)