diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 963acdc03d1f5..8a947e4505ec5 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -731,6 +731,7 @@ Datetimelike
 - Bug in :meth:`SeriesGroupBy.value_counts` index when passing categorical column (:issue:`44324`)
 - Bug in :meth:`DatetimeIndex.tz_localize` localizing to UTC failing to make a copy of the underlying data (:issue:`46460`)
 - Bug in :meth:`DatetimeIndex.resolution` incorrectly returning "day" instead of "nanosecond" for nanosecond-resolution indexes (:issue:`46903`)
+- Bug in :class:`Timestamp` with an integer or float value and ``unit="Y"`` or ``unit="M"`` giving slightly-wrong results (:issue:`47266`)
 -
 
 Timedelta
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index 44335836dc2ee..fe558d5c58368 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -250,6 +250,12 @@ cdef _TSObject convert_to_tsobject(object ts, tzinfo tz, str unit,
         if ts == NPY_NAT:
             obj.value = NPY_NAT
         else:
+            if unit in ["Y", "M"]:
+                # GH#47266 cast_from_unit leads to weird results e.g. with "Y"
+                #  and 150 we'd get 2120-01-01 09:00:00
+                ts = np.datetime64(ts, unit)
+                return convert_to_tsobject(ts, tz, None, False, False)
+
             ts = ts * cast_from_unit(None, unit)
             obj.value = ts
             dt64_to_dtstruct(ts, &obj.dts)
@@ -258,7 +264,11 @@ cdef _TSObject convert_to_tsobject(object ts, tzinfo tz, str unit,
             obj.value = NPY_NAT
         else:
             if unit in ["Y", "M"]:
-                if ts != int(ts):
+                if ts == int(ts):
+                    # GH#47266 Avoid cast_from_unit, which would give weird results
+                    #  e.g. with "Y" and 150.0 we'd get 2120-01-01 09:00:00
+                    return convert_to_tsobject(int(ts), tz, unit, False, False)
+                else:
                     # GH#47267 it is clear that 2 "M" corresponds to 1970-02-01,
                     #  but not clear what 2.5 "M" corresponds to, so we will
                     #  disallow that case.
diff --git a/pandas/tests/scalar/timestamp/test_constructors.py b/pandas/tests/scalar/timestamp/test_constructors.py
index daf1730df489d..7b3647dc6cbef 100644
--- a/pandas/tests/scalar/timestamp/test_constructors.py
+++ b/pandas/tests/scalar/timestamp/test_constructors.py
@@ -25,6 +25,19 @@
 
 
 class TestTimestampConstructors:
+    @pytest.mark.parametrize("typ", [int, float])
+    def test_constructor_int_float_with_YM_unit(self, typ):
+        # GH#47266 avoid the conversions in cast_from_unit
+        val = typ(150)
+
+        ts = Timestamp(val, unit="Y")
+        expected = Timestamp("2120-01-01")
+        assert ts == expected
+
+        ts = Timestamp(val, unit="M")
+        expected = Timestamp("1982-07-01")
+        assert ts == expected
+
     def test_constructor_float_not_round_with_YM_unit_deprecated(self):
         # GH#47267 avoid the conversions in cast_from-unit