diff --git a/django/db/backends/base/schema.py b/django/db/backends/base/schema.py
index d14f8919c0..d53836e62e 100644
--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -709,9 +709,9 @@ class BaseDatabaseSchemaEditor(object):
                 }
             )
         # Does it have a foreign key?
-        if new_field.rel and \
-           (fks_dropped or (old_field.rel and not old_field.db_constraint)) and \
-           new_field.db_constraint:
+        if (new_field.rel and
+                (fks_dropped or not old_field.rel or not old_field.db_constraint) and
+                new_field.db_constraint):
             self.execute(self._create_fk_sql(model, new_field, "_fk_%(to_table)s_%(to_column)s"))
         # Rebuild FKs that pointed to us if we previously had to drop them
         if old_field.primary_key and new_field.primary_key and old_type != new_type:
diff --git a/docs/releases/1.7.6.txt b/docs/releases/1.7.6.txt
index dd4412a783..e326cfb440 100644
--- a/docs/releases/1.7.6.txt
+++ b/docs/releases/1.7.6.txt
@@ -9,4 +9,8 @@ Django 1.7.6 fixes several bugs in 1.7.5.
 Bugfixes
 ========
 
-* ...
+* Fixed crash when coercing ``ManyRelatedManager`` to a string
+  (:ticket:`24352`).
+
+* Fixed a bug that prevented migrations from adding a FK constraint
+  for an existing column. (:ticket:`24447`).
diff --git a/tests/schema/tests.py b/tests/schema/tests.py
index 901397e391..2f4a84db09 100644
--- a/tests/schema/tests.py
+++ b/tests/schema/tests.py
@@ -545,6 +545,45 @@ class SchemaTests(TransactionTestCase):
         else:
             self.fail("No FK constraint for author_id found")
 
+    @unittest.skipUnless(connection.features.supports_foreign_keys, "No FK support")
+    def test_alter_to_fk(self):
+        """
+        #24447 - Tests adding a FK constraint for an existing column
+        """
+        class LocalBook(Model):
+            author = IntegerField()
+            title = CharField(max_length=100, db_index=True)
+            pub_date = DateTimeField()
+
+            class Meta:
+                app_label = 'schema'
+                apps = new_apps
+
+        self.local_models = [LocalBook]
+
+        # Create the tables
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+            editor.create_model(LocalBook)
+        # Ensure no FK constraint exists
+        constraints = self.get_constraints(LocalBook._meta.db_table)
+        for name, details in constraints.items():
+            if details['foreign_key']:
+                self.fail('Found an unexpected FK constraint to %s' % details['columns'])
+        old_field = LocalBook._meta.get_field("author")
+        new_field = ForeignKey(Author)
+        new_field.set_attributes_from_name("author")
+        with connection.schema_editor() as editor:
+            editor.alter_field(LocalBook, old_field, new_field, strict=True)
+        constraints = self.get_constraints(LocalBook._meta.db_table)
+        # Ensure FK constraint exists
+        for name, details in constraints.items():
+            if details['foreign_key'] and details['columns'] == ["author_id"]:
+                self.assertEqual(details['foreign_key'], ('schema_author', 'id'))
+                break
+        else:
+            self.fail("No FK constraint for author_id found")
+
     @unittest.skipUnless(connection.features.supports_foreign_keys, "No FK support")
     def test_alter_o2o_to_fk(self):
         """