diff --git a/src/marshmallow/utils.py b/src/marshmallow/utils.py
index bda3c06fc..3fd5e6769 100644
--- a/src/marshmallow/utils.py
+++ b/src/marshmallow/utils.py
@@ -41,17 +41,21 @@ def from_timestamp(value: typing.Any) -> dt.datetime:
     if value is True or value is False:
         raise ValueError("Not a valid POSIX timestamp")
     value = float(value)
-    if value < 0:
-        raise ValueError("Not a valid POSIX timestamp")
 
     # Load a timestamp with utc as timezone to prevent using system timezone.
-    # Then set timezone to None, to let the Field handle adding timezone info.
     try:
-        return dt.datetime.fromtimestamp(value, tz=dt.timezone.utc).replace(tzinfo=None)
+        ret_dt = dt.datetime.fromtimestamp(value, tz=dt.timezone.utc)
     except OverflowError as exc:
         raise ValueError("Timestamp is too large") from exc
-    except OSError as exc:
-        raise ValueError("Error converting value to datetime") from exc
+    except OSError:
+        try:
+            ret_dt = dt.datetime(1970, 1, 1, tzinfo=dt.timezone.utc) + dt.timedelta(
+                seconds=value
+            )
+        except OverflowError as exc:
+            raise ValueError("Timestamp is too large") from exc
+    # Then set timezone to None, to let the Field handle adding timezone info.
+    return ret_dt.replace(tzinfo=None)
 
 
 def from_timestamp_ms(value: typing.Any) -> dt.datetime:
diff --git a/tests/test_deserialization.py b/tests/test_deserialization.py
index eb7faa9ad..5fcf93c97 100644
--- a/tests/test_deserialization.py
+++ b/tests/test_deserialization.py
@@ -569,8 +569,10 @@ def test_iso_datetime_field_deserialization(self, fmt, value, expected, aware):
                 dt.datetime(2013, 11, 10, 0, 23, 45, 123456),
             ),
             ("timestamp", 1, dt.datetime(1970, 1, 1, 0, 0, 1)),
+            ("timestamp", -1, dt.datetime(1969, 12, 31, 23, 59, 59)),
             ("timestamp_ms", 1384043025000, dt.datetime(2013, 11, 10, 0, 23, 45)),
             ("timestamp_ms", 1000, dt.datetime(1970, 1, 1, 0, 0, 1)),
+            ("timestamp_ms", -1000, dt.datetime(1969, 12, 31, 23, 59, 59)),
         ],
     )
     def test_timestamp_field_deserialization(self, fmt, value, expected):
@@ -598,16 +600,14 @@ def test_boolean_timestamp_field_deserialization(self, fmt, in_value):
             field.deserialize(in_value)
 
     @pytest.mark.parametrize("fmt", ["timestamp", "timestamp_ms"])
-    @pytest.mark.parametrize(
-        "in_value",
-        ["", "!@#", -1],
-    )
+    @pytest.mark.parametrize("in_value", ["", "!@#"])
     def test_invalid_timestamp_field_deserialization(self, fmt, in_value):
         field = fields.DateTime(format=fmt)
         with pytest.raises(ValidationError, match="Not a valid datetime."):
             field.deserialize(in_value)
 
     # Regression test for https://github.com/marshmallow-code/marshmallow/pull/2102
+    # fromtimestamp may raise OSError or OverflowError depending on the platform.
     @pytest.mark.parametrize("fmt", ["timestamp", "timestamp_ms"])
     @pytest.mark.parametrize(
         "mock_fromtimestamp", [MockDateTimeOSError, MockDateTimeOverflowError]
@@ -618,6 +618,16 @@ def test_oversized_timestamp_field_deserialization(self, fmt, mock_fromtimestamp
             with pytest.raises(ValidationError, match="Not a valid datetime."):
                 field.deserialize(99999999999999999)
 
+    @pytest.mark.parametrize(
+        ("fmt", "val"), (("timestamp", -1), ("timestamp_ms", -1000))
+    )
+    def test_negative_timestamp_field_deserialization(self, fmt, val):
+        # OSError is raised on Windows for negative timestamps.
+        # Force it with a mock to test on any platform.
+        with patch("datetime.datetime", MockDateTimeOSError):
+            field = fields.DateTime(format=fmt)
+            assert field.deserialize(val) == dt.datetime(1969, 12, 31, 23, 59, 59)
+
     @pytest.mark.parametrize(
         ("fmt", "timezone", "value", "expected"),
         [
diff --git a/tests/test_utils.py b/tests/test_utils.py
index 26c12f6a7..f8aac416b 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -108,6 +108,8 @@ def test_is_collection():
     [
         (1676386740, dt.datetime(2023, 2, 14, 14, 59, 00)),
         (1676386740.58, dt.datetime(2023, 2, 14, 14, 59, 00, 580000)),
+        (-627296460, dt.datetime(1950, 2, 14, 14, 59, 00)),
+        (-627296459.42, dt.datetime(1950, 2, 14, 14, 59, 00, 580000)),
     ],
 )
 def test_from_timestamp(value, expected):
@@ -116,12 +118,6 @@ def test_from_timestamp(value, expected):
     assert result == expected
 
 
-def test_from_timestamp_with_negative_value():
-    value = -10
-    with pytest.raises(ValueError, match=r"Not a valid POSIX timestamp"):
-        utils.from_timestamp(value)
-
-
 def test_from_timestamp_with_overflow_value():
     value = 9223372036854775
     with pytest.raises(ValueError, match=r"out of range|year must be in 1\.\.9999"):