diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index 083242cd69b74..0097847874616 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -663,6 +663,7 @@ Timezones
 - Bug in tz-aware :class:`DatetimeIndex` where addition/subtraction with a :class:`TimedeltaIndex` or array with ``dtype='timedelta64[ns]'`` was incorrect (:issue:`17558`)
 - Bug in :func:`DatetimeIndex.insert` where inserting ``NaT`` into a timezone-aware index incorrectly raised (:issue:`16357`)
 - Bug in the :class:`DataFrame` constructor, where tz-aware Datetimeindex and a given column name will result in an empty ``DataFrame`` (:issue:`19157`)
+- Bug in :func:`Timestamp.tz_localize` where localizing a timestamp near the minimum or maximum valid values could overflow and return a timestamp with an incorrect nanosecond value (:issue:`12677`)
 
 Offsets
 ^^^^^^^
diff --git a/pandas/_libs/tslibs/conversion.pxd b/pandas/_libs/tslibs/conversion.pxd
index 6e7df10e7c424..59c1cde11f925 100644
--- a/pandas/_libs/tslibs/conversion.pxd
+++ b/pandas/_libs/tslibs/conversion.pxd
@@ -21,8 +21,6 @@ cdef convert_to_tsobject(object ts, object tz, object unit,
 cdef _TSObject convert_datetime_to_tsobject(datetime ts, object tz,
                                             int32_t nanos=*)
 
-cdef void _localize_tso(_TSObject obj, object tz)
-
 cpdef int64_t tz_convert_single(int64_t val, object tz1, object tz2)
 
 cdef int64_t get_datetime64_nanos(object val) except? -1
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index 4f1a053da6f1d..f37d71af0bd4d 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -309,12 +309,13 @@ cdef convert_to_tsobject(object ts, object tz, object unit,
         raise TypeError('Cannot convert input [{}] of type {} to '
                         'Timestamp'.format(ts, type(ts)))
 
-    if obj.value != NPY_NAT:
-        check_dts_bounds(&obj.dts)
-
     if tz is not None:
-        _localize_tso(obj, tz)
+        localize_tso(obj, tz)
 
+    if obj.value != NPY_NAT:
+        # check_overflows needs to run after localize_tso
+        check_dts_bounds(&obj.dts)
+        check_overflows(obj)
     return obj
 
 
@@ -391,6 +392,7 @@ cdef _TSObject convert_datetime_to_tsobject(datetime ts, object tz,
         obj.dts.ps = nanos * 1000
 
     check_dts_bounds(&obj.dts)
+    check_overflows(obj)
     return obj
 
 
@@ -454,6 +456,7 @@ cdef _TSObject convert_str_to_tsobject(object ts, object tz, object unit,
                 obj.value = tz_convert_single(obj.value, obj.tzinfo, 'UTC')
                 if tz is None:
                     check_dts_bounds(&obj.dts)
+                    check_overflows(obj)
                     return obj
                 else:
                     # Keep the converter same as PyDateTime's
@@ -469,7 +472,7 @@ cdef _TSObject convert_str_to_tsobject(object ts, object tz, object unit,
             else:
                 ts = obj.value
                 if tz is not None:
-                    # shift for _localize_tso
+                    # shift for localize_tso
                     ts = tz_localize_to_utc(np.array([ts], dtype='i8'), tz,
                                             ambiguous='raise',
                                             errors='raise')[0]
@@ -490,12 +493,51 @@ cdef _TSObject convert_str_to_tsobject(object ts, object tz, object unit,
     return convert_to_tsobject(ts, tz, unit, dayfirst, yearfirst)
 
 
+cdef inline check_overflows(_TSObject obj):
+    """
+    Check that we haven't silently overflowed in timezone conversion
+    
+    Parameters
+    ----------
+    obj : _TSObject
+
+    Returns
+    -------
+    None
+
+    Raises
+    ------
+    OutOfBoundsDatetime
+    """
+    # GH#12677
+    if obj.dts.year == 1677:
+        if not (obj.value < 0):
+            raise OutOfBoundsDatetime
+    elif obj.dts.year == 2262:
+        if not (obj.value > 0):
+            raise OutOfBoundsDatetime
+
+
 # ----------------------------------------------------------------------
 # Localization
 
-cdef inline void _localize_tso(_TSObject obj, object tz):
+cdef inline void localize_tso(_TSObject obj, tzinfo tz):
     """
-    Take a TSObject in UTC and localizes to timezone tz.
+    Given the UTC nanosecond timestamp in obj.value, find the wall-clock
+    representation of that timestamp in the given timezone.
+
+    Parameters
+    ----------
+    obj : _TSObject
+    tz : tzinfo
+
+    Returns
+    -------
+    None
+
+    Notes
+    -----
+    Sets obj.tzinfo inplace, alters obj.dts inplace.
     """
     cdef:
         ndarray[int64_t] trans, deltas
diff --git a/pandas/tests/scalar/timestamp/test_timezones.py b/pandas/tests/scalar/timestamp/test_timezones.py
index 7a5c6feb8b651..f43651dc6f0db 100644
--- a/pandas/tests/scalar/timestamp/test_timezones.py
+++ b/pandas/tests/scalar/timestamp/test_timezones.py
@@ -15,12 +15,29 @@
 import pandas.util._test_decorators as td
 
 from pandas import Timestamp, NaT
+from pandas.errors import OutOfBoundsDatetime
 
 
 class TestTimestampTZOperations(object):
     # --------------------------------------------------------------
     # Timestamp.tz_localize
 
+    def test_tz_localize_pushes_out_of_bounds(self):
+        # GH#12677
+        # tz_localize that pushes away from the boundary is OK
+        pac = Timestamp.min.tz_localize('US/Pacific')
+        assert pac.value > Timestamp.min.value
+        pac.tz_convert('Asia/Tokyo')  # tz_convert doesn't change value
+        with pytest.raises(OutOfBoundsDatetime):
+            Timestamp.min.tz_localize('Asia/Tokyo')
+
+        # tz_localize that pushes away from the boundary is OK
+        tokyo = Timestamp.max.tz_localize('Asia/Tokyo')
+        assert tokyo.value < Timestamp.max.value
+        tokyo.tz_convert('US/Pacific')  # tz_convert doesn't change value
+        with pytest.raises(OutOfBoundsDatetime):
+            Timestamp.max.tz_localize('US/Pacific')
+
     def test_tz_localize_ambiguous_bool(self):
         # make sure that we are correctly accepting bool values as ambiguous
         # GH#14402