diff --git a/doc/source/whatsnew/v0.21.0.txt b/doc/source/whatsnew/v0.21.0.txt
index 5003aa0d97c1c..43e90f06ed504 100644
--- a/doc/source/whatsnew/v0.21.0.txt
+++ b/doc/source/whatsnew/v0.21.0.txt
@@ -498,6 +498,7 @@ Conversion
 - Bug in :func:`Series.fillna` returns frame when ``inplace=True`` and ``value`` is dict (:issue:`16156`)
 - Bug in :attr:`Timestamp.weekday_name` returning a UTC-based weekday name when localized to a timezone (:issue:`17354`)
 - Bug in ``Timestamp.replace`` when replacing ``tzinfo`` around DST changes (:issue:`15683`)
+- Bug in ``Timedelta`` construction and arithmetic that would not propagate the ``Overflow`` exception (:issue:`17367`)
 
 Indexing
 ^^^^^^^^
diff --git a/pandas/_libs/tslib.pyx b/pandas/_libs/tslib.pyx
index 6ba37062ac869..077603af96947 100644
--- a/pandas/_libs/tslib.pyx
+++ b/pandas/_libs/tslib.pyx
@@ -3514,7 +3514,7 @@ cpdef convert_to_timedelta64(object ts, object unit):
         ts = np.timedelta64(_delta_to_nanoseconds(ts), 'ns')
 
     if isinstance(ts, timedelta):
-        ts = np.timedelta64(ts)
+        ts = np.timedelta64(_delta_to_nanoseconds(ts), 'ns')
     elif not isinstance(ts, np.timedelta64):
         raise ValueError("Invalid type for timedelta "
                          "scalar: %s" % type(ts))
@@ -3891,8 +3891,7 @@ for _maybe_method_name in dir(NaTType):
 #----------------------------------------------------------------------
 # Conversion routines
 
-
-cpdef int64_t _delta_to_nanoseconds(delta):
+cpdef int64_t _delta_to_nanoseconds(delta) except? -1:
     if isinstance(delta, np.ndarray):
         return delta.astype('m8[ns]').astype('int64')
     if hasattr(delta, 'nanos'):
@@ -3903,6 +3902,7 @@ cpdef int64_t _delta_to_nanoseconds(delta):
         return delta.astype("timedelta64[ns]").item()
     if is_integer_object(delta):
         return delta
+
     return (delta.days * 24 * 60 * 60 * 1000000
             + delta.seconds * 1000000
             + delta.microseconds) * 1000
diff --git a/pandas/tests/indexes/datetimes/test_tools.py b/pandas/tests/indexes/datetimes/test_tools.py
index be27334384f6b..e0ccedb834adf 100644
--- a/pandas/tests/indexes/datetimes/test_tools.py
+++ b/pandas/tests/indexes/datetimes/test_tools.py
@@ -787,6 +787,13 @@ def test_to_datetime_freq(self):
         assert xp.freq == rs.freq
         assert xp.tzinfo == rs.tzinfo
 
+    def test_to_datetime_overflow(self):
+        # gh-17637
+        # we are overflowing Timedelta range here
+
+        with pytest.raises(OverflowError):
+            date_range(start='1/1/1700', freq='B', periods=100000)
+
     def test_string_na_nat_conversion(self):
         # GH #999, #858
 
diff --git a/pandas/tests/scalar/test_timedelta.py b/pandas/tests/scalar/test_timedelta.py
index bc9a0388df9d9..2cabbfacf6416 100644
--- a/pandas/tests/scalar/test_timedelta.py
+++ b/pandas/tests/scalar/test_timedelta.py
@@ -166,6 +166,13 @@ def test_overflow_on_construction(self):
         value = pd.Timedelta('1day').value * 20169940
         pytest.raises(OverflowError, pd.Timedelta, value)
 
+        # xref gh-17637
+        with pytest.raises(OverflowError):
+            pd.Timedelta(7 * 19999, unit='D')
+
+        with pytest.raises(OverflowError):
+            pd.Timedelta(timedelta(days=13 * 19999))
+
     def test_total_seconds_scalar(self):
         # see gh-10939
         rng = Timedelta('1 days, 10:11:12.100123456')
@@ -612,6 +619,14 @@ def test_timedelta_arithmetic(self):
             tm.assert_series_equal(result_operator, expected)
             tm.assert_series_equal(result_method, expected)
 
+    def test_arithmetic_overflow(self):
+
+        with pytest.raises(OverflowError):
+            pd.Timestamp('1700-01-01') + pd.Timedelta(13 * 19999, unit='D')
+
+        with pytest.raises(OverflowError):
+            pd.Timestamp('1700-01-01') + timedelta(days=13 * 19999)
+
     def test_apply_to_timedelta(self):
         timedelta_NaT = pd.to_timedelta('NaT')