diff --git a/doc/source/whatsnew/v0.24.0.rst b/doc/source/whatsnew/v0.24.0.rst
index 3950ff3c8863d..6bb27d03835d7 100644
--- a/doc/source/whatsnew/v0.24.0.rst
+++ b/doc/source/whatsnew/v0.24.0.rst
@@ -1614,6 +1614,7 @@ Timedelta
 - Bug in :class:`Timedelta` and :func:`to_timedelta()` have inconsistencies in supported unit string (:issue:`21762`)
 - Bug in :class:`TimedeltaIndex` division where dividing by another :class:`TimedeltaIndex` raised ``TypeError`` instead of returning a :class:`Float64Index` (:issue:`23829`, :issue:`22631`)
 - Bug in :class:`TimedeltaIndex` comparison operations where comparing against non-``Timedelta``-like objects would raise ``TypeError`` instead of returning all-``False`` for ``__eq__`` and all-``True`` for ``__ne__`` (:issue:`24056`)
+- Bug in :class:`Timedelta` comparisons when comparing with a ``Tick`` object incorrectly raising ``TypeError`` (:issue:`24710`)
 
 Timezones
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index c2f51436612a4..7097a702227d7 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -5,6 +5,7 @@ import cython
 import time
 from cpython.datetime cimport (PyDateTime_IMPORT,
                                PyDateTime_Check,
+                               PyDelta_Check,
                                datetime, timedelta,
                                time as dt_time)
 PyDateTime_IMPORT
@@ -28,6 +29,9 @@ from pandas._libs.tslibs.np_datetime cimport (
     npy_datetimestruct, dtstruct_to_dt64, dt64_to_dtstruct)
 from pandas._libs.tslibs.timezones import UTC
 
+
+PY2 = bytes == str
+
 # ---------------------------------------------------------------------
 # Constants
 
@@ -126,6 +130,26 @@ def apply_index_wraps(func):
     return wrapper
 
 
+cdef _wrap_timedelta_result(result):
+    """
+    Tick operations dispatch to their Timedelta counterparts.  Wrap the result
+    of these operations in a Tick if possible.
+
+    Parameters
+    ----------
+    result : object
+
+    Returns
+    -------
+    object
+    """
+    if PyDelta_Check(result):
+        # convert Timedelta back to a Tick
+        from pandas.tseries.offsets import _delta_to_tick
+        return _delta_to_tick(result)
+
+    return result
+
 # ---------------------------------------------------------------------
 # Business Helpers
 
@@ -508,7 +532,13 @@ class _Tick(object):
     dummy class to mix into tseries.offsets.Tick so that in tslibs.period we
     can do isinstance checks on _Tick and avoid importing tseries.offsets
     """
-    pass
+
+    def __truediv__(self, other):
+        result = self.delta.__truediv__(other)
+        return _wrap_timedelta_result(result)
+
+    if PY2:
+        __div__ = __truediv__
 
 
 # ----------------------------------------------------------------------
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 037e7de27adc3..0476ba1c78efc 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -36,6 +36,7 @@ from pandas._libs.tslibs.nattype import nat_strings
 from pandas._libs.tslibs.nattype cimport (
     checknull_with_nat, NPY_NAT, c_NaT as NaT)
 from pandas._libs.tslibs.offsets cimport to_offset
+from pandas._libs.tslibs.offsets import _Tick as Tick
 
 # ----------------------------------------------------------------------
 # Constants
@@ -757,7 +758,7 @@ cdef class _Timedelta(timedelta):
 
         if isinstance(other, _Timedelta):
             ots = other
-        elif PyDelta_Check(other):
+        elif PyDelta_Check(other) or isinstance(other, Tick):
             ots = Timedelta(other)
         else:
             ndim = getattr(other, "ndim", -1)
diff --git a/pandas/tests/arithmetic/test_numeric.py b/pandas/tests/arithmetic/test_numeric.py
index 7afb90978131d..6694946902836 100644
--- a/pandas/tests/arithmetic/test_numeric.py
+++ b/pandas/tests/arithmetic/test_numeric.py
@@ -149,10 +149,6 @@ def test_numeric_arr_mul_tdscalar(self, scalar_td, numeric_idx, box):
         tm.assert_equal(commute, expected)
 
     def test_numeric_arr_rdiv_tdscalar(self, three_days, numeric_idx, box):
-
-        if box is not pd.Index and isinstance(three_days, pd.offsets.Tick):
-            raise pytest.xfail("Tick division not implemented")
-
         index = numeric_idx[1:3]
 
         expected = TimedeltaIndex(['3 Days', '36 Hours'])
diff --git a/pandas/tests/scalar/timedelta/test_timedelta.py b/pandas/tests/scalar/timedelta/test_timedelta.py
index db0c848eaeb4b..bc753c45c803a 100644
--- a/pandas/tests/scalar/timedelta/test_timedelta.py
+++ b/pandas/tests/scalar/timedelta/test_timedelta.py
@@ -78,6 +78,27 @@ def test_unary_ops(self):
 
 
 class TestTimedeltaComparison(object):
+    def test_compare_tick(self, tick_classes):
+        cls = tick_classes
+
+        off = cls(4)
+        td = off.delta
+        assert isinstance(td, Timedelta)
+
+        assert td == off
+        assert not td != off
+        assert td <= off
+        assert td >= off
+        assert not td < off
+        assert not td > off
+
+        assert not td == 2 * off
+        assert td != 2 * off
+        assert td <= 2 * off
+        assert td < 2 * off
+        assert not td >= 2 * off
+        assert not td > 2 * off
+
     def test_comparison_object_array(self):
         # analogous to GH#15183
         td = Timedelta('2 days')
diff --git a/pandas/tests/tseries/offsets/test_ticks.py b/pandas/tests/tseries/offsets/test_ticks.py
index 27ec7d9d9093a..f4b012ec1897f 100644
--- a/pandas/tests/tseries/offsets/test_ticks.py
+++ b/pandas/tests/tseries/offsets/test_ticks.py
@@ -2,6 +2,8 @@
 """
 Tests for offsets.Tick and subclasses
 """
+from __future__ import division
+
 from datetime import datetime, timedelta
 
 from hypothesis import assume, example, given, settings, strategies as st
@@ -36,6 +38,10 @@ def test_delta_to_tick():
     tick = offsets._delta_to_tick(delta)
     assert (tick == offsets.Day(3))
 
+    td = Timedelta(nanoseconds=5)
+    tick = offsets._delta_to_tick(td)
+    assert tick == Nano(5)
+
 
 @pytest.mark.parametrize('cls', tick_classes)
 @settings(deadline=None)  # GH 24641
@@ -228,6 +234,34 @@ def test_tick_addition(kls, expected):
     assert result == expected
 
 
+@pytest.mark.parametrize('cls', tick_classes)
+def test_tick_division(cls):
+    off = cls(10)
+
+    assert off / cls(5) == 2
+    assert off / 2 == cls(5)
+    assert off / 2.0 == cls(5)
+
+    assert off / off.delta == 1
+    assert off / off.delta.to_timedelta64() == 1
+
+    assert off / Nano(1) == off.delta / Nano(1).delta
+
+    if cls is not Nano:
+        # A case where we end up with a smaller class
+        result = off / 1000
+        assert isinstance(result, offsets.Tick)
+        assert not isinstance(result, cls)
+        assert result.delta == off.delta / 1000
+
+    if cls._inc < Timedelta(seconds=1):
+        # Case where we end up with a bigger class
+        result = off / .001
+        assert isinstance(result, offsets.Tick)
+        assert not isinstance(result, cls)
+        assert result.delta == off.delta / .001
+
+
 @pytest.mark.parametrize('cls1', tick_classes)
 @pytest.mark.parametrize('cls2', tick_classes)
 def test_tick_zero(cls1, cls2):
diff --git a/pandas/tseries/offsets.py b/pandas/tseries/offsets.py
index 73f85d954432e..f208ce37a3b14 100644
--- a/pandas/tseries/offsets.py
+++ b/pandas/tseries/offsets.py
@@ -2343,7 +2343,8 @@ def isAnchored(self):
 
 
 def _delta_to_tick(delta):
-    if delta.microseconds == 0:
+    if delta.microseconds == 0 and getattr(delta, "nanoseconds", 0) == 0:
+        # nanoseconds only for pd.Timedelta
         if delta.seconds == 0:
             return Day(delta.days)
         else: