diff --git a/docs/src/whatsnew/latest.rst b/docs/src/whatsnew/latest.rst
index 0c1b8292b5..8c666c2d5d 100644
--- a/docs/src/whatsnew/latest.rst
+++ b/docs/src/whatsnew/latest.rst
@@ -42,8 +42,9 @@ This document explains the changes made to Iris for this release
 💣 Incompatible Changes
 =======================
 
-#. N/A
-
+#. `@bouweandela`_ changed the ``convert_units`` method on cubes and coordinates
+   so it also converts the values of the attributes ``"actual_range"``,
+   ``"valid_max"``, ``"valid_min"``, and ``"valid_range"``. (:pull:`6416`)
 
 🚀 Performance Enhancements
 ===========================
diff --git a/lib/iris/coords.py b/lib/iris/coords.py
index ca73dcb729..9fdd20d6fc 100644
--- a/lib/iris/coords.py
+++ b/lib/iris/coords.py
@@ -747,6 +747,9 @@ def pointwise_convert(values):
             else:
                 new_bounds = self.units.convert(self.bounds, unit)
             self.bounds = new_bounds
+        for key in "actual_range", "valid_max", "valid_min", "valid_range":
+            if key in self.attributes:
+                self.attributes[key] = self.units.convert(self.attributes[key], unit)
         self.units = unit
 
     def is_compatible(self, other, ignore=None):
diff --git a/lib/iris/cube.py b/lib/iris/cube.py
index 77191c3a9a..be8ddcfc47 100644
--- a/lib/iris/cube.py
+++ b/lib/iris/cube.py
@@ -1478,6 +1478,11 @@ def convert_units(self, unit: str | Unit) -> None:
         else:
             new_data = self.units.convert(self.data, unit)
         self.data = new_data
+        for key in "actual_range", "valid_max", "valid_min", "valid_range":
+            if key in self.attributes.locals:
+                self.attributes.locals[key] = self.units.convert(
+                    self.attributes.locals[key], unit
+                )
         self.units = unit
 
     def add_cell_method(self, cell_method: CellMethod) -> None:
diff --git a/lib/iris/tests/unit/coords/test_Coord.py b/lib/iris/tests/unit/coords/test_Coord.py
index 97429f58f8..ba77379a50 100644
--- a/lib/iris/tests/unit/coords/test_Coord.py
+++ b/lib/iris/tests/unit/coords/test_Coord.py
@@ -23,6 +23,7 @@
 from iris.coords import AuxCoord, Coord, DimCoord
 from iris.cube import Cube
 from iris.exceptions import UnitConversionError
+from iris.tests import _shared_utils
 from iris.tests.unit.coords import CoordTestMixin
 from iris.warnings import IrisVagueMetadataWarning
 
@@ -1177,16 +1178,35 @@ def test_coord_3d(self):
             coord._sanity_check_bounds()
 
 
-class Test_convert_units(tests.IrisTest):
+class Test_convert_units:
     def test_convert_unknown_units(self):
         coord = iris.coords.AuxCoord(1, units="unknown")
         emsg = (
             "Cannot convert from unknown units. "
             'The "units" attribute may be set directly.'
         )
-        with self.assertRaisesRegex(UnitConversionError, emsg):
+        with pytest.raises(UnitConversionError, match=emsg):
             coord.convert_units("degrees")
 
+    @pytest.mark.parametrize(
+        "attribute",
+        [
+            "valid_min",
+            "valid_max",
+            "valid_range",
+            "actual_range",
+        ],
+    )
+    def test_convert_attributes(self, attribute):
+        coord = iris.coords.AuxCoord(1, units="m")
+        value = np.array([0, 10]) if attribute.endswith("range") else 0
+        coord.attributes[attribute] = value
+        coord.convert_units("ft")
+        converted_value = cf_units.Unit("m").convert(value, "ft")
+        _shared_utils.assert_array_all_close(
+            coord.attributes[attribute], converted_value
+        )
+
 
 class Test___str__(tests.IrisTest):
     def test_short_time_interval(self):
diff --git a/lib/iris/tests/unit/cube/test_Cube.py b/lib/iris/tests/unit/cube/test_Cube.py
index 21fa27d2f9..0652ab9d59 100644
--- a/lib/iris/tests/unit/cube/test_Cube.py
+++ b/lib/iris/tests/unit/cube/test_Cube.py
@@ -3024,6 +3024,25 @@ def test_unit_multiply(self):
         cube.data
         _client.close()
 
+    @pytest.mark.parametrize(
+        "attribute",
+        [
+            "valid_min",
+            "valid_max",
+            "valid_range",
+            "actual_range",
+        ],
+    )
+    def test_convert_attributes(self, attribute):
+        cube = iris.cube.Cube(1, units="degrees_C")
+        value = np.array([0, 10]) if attribute.endswith("range") else 0
+        cube.attributes.locals[attribute] = value
+        cube.convert_units("K")
+        converted_value = Unit("degrees_C").convert(value, "K")
+        _shared_utils.assert_array_all_close(
+            cube.attributes.locals[attribute], converted_value
+        )
+
 
 class Test__eq__data:
     """Partial cube equality testing, for data type only."""