diff --git a/CHANGES.rst b/CHANGES.rst
index 6f0cce2a..d9e241d2 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -15,6 +15,8 @@
 
 - Force ``bounding_box`` to always be returned as a ``F`` ordered box. [#522] 
 
+- Adjust ``world_to_array_index_values`` to round to integer coordinates as specified by APE 14. [#525]
+
 0.21.0 (2024-03-10)
 -------------------
 
diff --git a/gwcs/api.py b/gwcs/api.py
index 4f2ce9fc..2b1ca22e 100644
--- a/gwcs/api.py
+++ b/gwcs/api.py
@@ -147,10 +147,14 @@ def world_to_array_index_values(self, *world_arrays):
         `~BaseLowLevelWCS.pixel_to_world_values`). The indices should be
         returned as rounded integers.
         """
-        result = self.world_to_pixel_values(*world_arrays)
-        if self.pixel_n_dim != 1:
-            result = result[::-1]
-        return result
+        results = self.world_to_pixel_values(*world_arrays)
+        if self.pixel_n_dim == 1:
+            results = (results,)
+        else:
+            results = results[::-1]
+
+        results = tuple(utils._toindex(result) for result in results)
+        return results[0] if self.pixel_n_dim == 1 else results
 
     @property
     def array_shape(self):