diff --git a/django/db/backends/sqlite3/schema.py b/django/db/backends/sqlite3/schema.py
index 69607b292a..40efa822b1 100644
--- a/django/db/backends/sqlite3/schema.py
+++ b/django/db/backends/sqlite3/schema.py
@@ -43,7 +43,8 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
         else:
             raise ValueError("Cannot quote parameter value %r of type %s" % (value, type(value)))
 
-    def _remake_table(self, model, create_fields=[], delete_fields=[], alter_fields=[], override_uniques=None):
+    def _remake_table(self, model, create_fields=[], delete_fields=[], alter_fields=[], override_uniques=None,
+                      override_indexes=None):
         """
         Shortcut to transform a model from old_model into new_model
         """
@@ -110,11 +111,20 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
                 for unique in model._meta.unique_together
             ]
 
+        # Work out the new value for index_together, taking renames into
+        # account
+        if override_indexes is None:
+            override_indexes = [
+                [rename_mapping.get(n, n) for n in index]
+                for index in model._meta.index_together
+            ]
+
         # Construct a new model for the new state
         meta_contents = {
             'app_label': model._meta.app_label,
             'db_table': model._meta.db_table + "__new",
             'unique_together': override_uniques,
+            'index_together': override_indexes,
             'apps': apps,
         }
         meta = type("Meta", tuple(), meta_contents)
@@ -190,6 +200,14 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
         # Alter by remaking table
         self._remake_table(model, alter_fields=[(old_field, new_field)])
 
+    def alter_index_together(self, model, old_index_together, new_index_together):
+        """
+        Deals with a model changing its index_together.
+        Note: The input index_togethers must be doubly-nested, not the single-
+        nested ["foo", "bar"] format.
+        """
+        self._remake_table(model, override_indexes=new_index_together)
+
     def alter_unique_together(self, model, old_unique_together, new_unique_together):
         """
         Deals with a model changing its unique_together.
diff --git a/docs/releases/1.7.2.txt b/docs/releases/1.7.2.txt
index ab548f4fab..9ed58bb217 100644
--- a/docs/releases/1.7.2.txt
+++ b/docs/releases/1.7.2.txt
@@ -89,3 +89,5 @@ Bugfixes
 
 * Fixed an infinite loop bug for certain cyclic migration dependencies, and made
   the error message for cyclic dependencies much more helpful.
+
+* Added missing ``index_together`` handling for SQLite (:ticket:`23880`).
diff --git a/tests/migrations/test_operations.py b/tests/migrations/test_operations.py
index 32f70e8fe8..ef6cbfc688 100644
--- a/tests/migrations/test_operations.py
+++ b/tests/migrations/test_operations.py
@@ -1052,16 +1052,14 @@ class OperationTests(OperationTestBase):
                     cursor.execute("INSERT INTO test_rnfl_pony (blue, weight) VALUES (1, 1)")
             cursor.execute("DELETE FROM test_rnfl_pony")
         # Ensure the index constraint has been ported over
-        # TODO: Uncomment assert when #23880 is fixed
-        # self.assertIndexExists("test_rnfl_pony", ["weight", "blue"])
+        self.assertIndexExists("test_rnfl_pony", ["weight", "blue"])
         # And test reversal
         with connection.schema_editor() as editor:
             operation.database_backwards("test_rnfl", editor, new_state, project_state)
         self.assertColumnExists("test_rnfl_pony", "pink")
         self.assertColumnNotExists("test_rnfl_pony", "blue")
         # Ensure the index constraint has been reset
-        # TODO: Uncomment assert when #23880 is fixed
-        # self.assertIndexExists("test_rnfl_pony", ["weight", "pink"])
+        self.assertIndexExists("test_rnfl_pony", ["weight", "pink"])
         # And deconstruction
         definition = operation.deconstruct()
         self.assertEqual(definition[0], "RenameField")