diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index f7faeea7a646f..2b1a61186dca6 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -502,7 +502,7 @@ Other Deprecations
   Use the public attributes :attr:`~RangeIndex.start`, :attr:`~RangeIndex.stop` and :attr:`~RangeIndex.step` instead (:issue:`26581`).
 - The :meth:`Series.ftype`, :meth:`Series.ftypes` and :meth:`DataFrame.ftypes` methods are deprecated and will be removed in a future version.
   Instead, use :meth:`Series.dtype` and :meth:`DataFrame.dtypes` (:issue:`26705`).
-
+- :meth:`Timedelta.resolution` is deprecated and replaced with :meth:`Timedelta.resolution_string`.  In a future version, :meth:`Timedelta.resolution` will be changed to behave like the standard library :attr:`timedelta.resolution` (:issue:`21344`)
 
 .. _whatsnew_0250.prior_deprecations:
 
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index ad60165e98d4f..6a32553fe2d38 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -950,7 +950,7 @@ cdef class _Timedelta(timedelta):
         return np.int64(self.value).view('m8[ns]')
 
     @property
-    def resolution(self):
+    def resolution_string(self):
         """
         Return a string representing the lowest timedelta resolution.
 
@@ -991,7 +991,6 @@ cdef class _Timedelta(timedelta):
         >>> td.resolution
         'U'
         """
-
         self._ensure_components()
         if self._ns:
             return "N"
@@ -1008,6 +1007,56 @@ cdef class _Timedelta(timedelta):
         else:
             return "D"
 
+    @property
+    def resolution(self):
+        """
+        Return a string representing the lowest timedelta resolution.
+
+        Each timedelta has a defined resolution that represents the lowest OR
+        most granular level of precision. Each level of resolution is
+        represented by a short string as defined below:
+
+        Resolution:     Return value
+
+        * Days:         'D'
+        * Hours:        'H'
+        * Minutes:      'T'
+        * Seconds:      'S'
+        * Milliseconds: 'L'
+        * Microseconds: 'U'
+        * Nanoseconds:  'N'
+
+        Returns
+        -------
+        str
+            Timedelta resolution.
+
+        Examples
+        --------
+        >>> td = pd.Timedelta('1 days 2 min 3 us 42 ns')
+        >>> td.resolution
+        'N'
+
+        >>> td = pd.Timedelta('1 days 2 min 3 us')
+        >>> td.resolution
+        'U'
+
+        >>> td = pd.Timedelta('2 min 3 s')
+        >>> td.resolution
+        'S'
+
+        >>> td = pd.Timedelta(36, unit='us')
+        >>> td.resolution
+        'U'
+        """
+        # See GH#21344
+        warnings.warn("Timedelta.resolution is deprecated, in a future "
+                      "version will behave like the standard library "
+                      "datetime.timedelta.resolution attribute.  "
+                      "Use Timedelta.resolution_string instead.",
+                      FutureWarning)
+        return self.resolution_string
+
     @property
     def nanoseconds(self):
         """
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index f5362c0b6bb5d..ba5507fa71e8c 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -551,11 +551,11 @@ def _maybe_cast_slice_bound(self, label, side, kind):
 
         if isinstance(label, str):
             parsed = Timedelta(label)
-            lbound = parsed.round(parsed.resolution)
+            lbound = parsed.round(parsed.resolution_string)
             if side == 'left':
                 return lbound
             else:
-                return (lbound + to_offset(parsed.resolution) -
+                return (lbound + to_offset(parsed.resolution_string) -
                         Timedelta(1, 'ns'))
         elif ((is_integer(label) or is_float(label)) and
               not is_timedelta64_dtype(label)):
diff --git a/pandas/tests/scalar/test_nat.py b/pandas/tests/scalar/test_nat.py
index 0ae4d107d85bd..19426c3bf3ffb 100644
--- a/pandas/tests/scalar/test_nat.py
+++ b/pandas/tests/scalar/test_nat.py
@@ -142,8 +142,8 @@ def test_nat_iso_format(get_nat):
 
 @pytest.mark.parametrize("klass,expected", [
     (Timestamp, ["freqstr", "normalize", "to_julian_date", "to_period", "tz"]),
-    (Timedelta, ["components", "delta", "is_populated", "to_pytimedelta",
-                 "to_timedelta64", "view"])
+    (Timedelta, ["components", "delta", "is_populated", "resolution_string",
+                 "to_pytimedelta", "to_timedelta64", "view"])
 ])
 def test_missing_public_nat_methods(klass, expected):
     # see gh-17327
diff --git a/pandas/tests/scalar/timedelta/test_timedelta.py b/pandas/tests/scalar/timedelta/test_timedelta.py
index 57b3705640202..f10876531e66a 100644
--- a/pandas/tests/scalar/timedelta/test_timedelta.py
+++ b/pandas/tests/scalar/timedelta/test_timedelta.py
@@ -742,6 +742,22 @@ def test_components(self):
         assert not result.iloc[0].isna().all()
         assert result.iloc[1].isna().all()
 
+    def test_resolution_string(self):
+        assert Timedelta(days=1).resolution_string == 'D'
+        assert Timedelta(days=1, hours=6).resolution_string == 'H'
+        assert Timedelta(days=1, minutes=6).resolution_string == 'T'
+        assert Timedelta(days=1, seconds=6).resolution_string == 'S'
+        assert Timedelta(days=1, milliseconds=6).resolution_string == 'L'
+        assert Timedelta(days=1, microseconds=6).resolution_string == 'U'
+        assert Timedelta(days=1, nanoseconds=6).resolution_string == 'N'
+
+    def test_resolution_deprecated(self):
+        # GH#21344
+        td = Timedelta(days=4, hours=3)
+        with tm.assert_produces_warning(FutureWarning) as w:
+            td.resolution
+        assert "Use Timedelta.resolution_string instead" in str(w[0].message)
+
 
 @pytest.mark.parametrize('value, expected', [
     (Timedelta('10S'), True),