diff --git a/arrow/parser.py b/arrow/parser.py
index fc3774b09..07f90d64d 100644
--- a/arrow/parser.py
+++ b/arrow/parser.py
@@ -713,7 +713,7 @@ def _build_datetime(parts: _Parts) -> datetime:
                 # day not given, default to 1
                 _day = 1
 
-            date_string = f"{year}-{week}-{_day}"
+            date_string = f"{year:04d}-{week}-{_day}"
 
             #  tokens for ISO 8601 weekdates
             dt = datetime.strptime(date_string, "%G-%V-%u")
@@ -750,7 +750,7 @@ def _build_datetime(parts: _Parts) -> datetime:
                     "Month component is not allowed with the DDD and DDDD tokens."
                 )
 
-            date_string = f"{_year}-{day_of_year}"
+            date_string = f"{_year:04d}-{day_of_year}"
             try:
                 dt = datetime.strptime(date_string, "%Y-%j")
             except ValueError:
diff --git a/tests/test_parser.py b/tests/test_parser.py
index 7038d880f..4fba59c2d 100644
--- a/tests/test_parser.py
+++ b/tests/test_parser.py
@@ -716,6 +716,20 @@ def test_parse_HH_24(self):
         with pytest.raises(ParserError):
             self.parser.parse("2019-12-31T24:00:00.999999", "YYYY-MM-DDTHH:mm:ss.S")
 
+    @pytest.mark.parametrize("year", [1, 4, 12, 99, 400, 999, 1000, 2024])
+    @pytest.mark.parametrize("token", ["DDD", "DDDD"])
+    def test_parse_low_year_ordinal(self, year, token):
+        ordinal = "2" if token == "DDD" else "002"
+        value = f"{year:04d}-{ordinal}"
+        assert self.parser.parse(value, f"YYYY-{token}") == datetime(year, 1, 2)
+
+    @pytest.mark.parametrize("year", [1, 4, 12, 99, 400, 999, 1000, 2024])
+    def test_parse_low_year_iso_week(self, year):
+        value = f"{year:04d}-W01-1"
+        expected = datetime.fromisocalendar(year, 1, 1)
+        assert self.parser.parse(value, "W") == expected
+        assert arrow.get(value) == arrow.Arrow.fromdatetime(expected)
+
     def test_parse_W(self):
         assert self.parser.parse("2011-W05-4", "W") == datetime(2011, 2, 3)
         assert self.parser.parse("2011W054", "W") == datetime(2011, 2, 3)