diff --git a/gtk/gtkmenubutton.c b/gtk/gtkmenubutton.c
index 02eb13b4a0..6552165824 100644
--- a/gtk/gtkmenubutton.c
+++ b/gtk/gtkmenubutton.c
@@ -669,6 +669,10 @@ gtk_menu_button_init (GtkMenuButton *self)
   gtk_widget_set_sensitive (self->button, FALSE);
 
   gtk_widget_add_css_class (GTK_WIDGET (self), "popup");
+
+  gtk_accessible_update_relation (GTK_ACCESSIBLE (self->button), GTK_ACCESSIBLE_RELATION_LABELLED_BY, self, NULL,
+  GTK_ACCESSIBLE_RELATION_DESCRIBED_BY, self, NULL,
+                                  -1);
 }
 
 static GtkBuildableIface *parent_buildable_iface;
@@ -1017,6 +1021,9 @@ gtk_menu_button_set_icon_name (GtkMenuButton *menu_button,
   box = gtk_box_new (GTK_ORIENTATION_HORIZONTAL, 0);
   gtk_widget_set_halign (box, GTK_ALIGN_CENTER);
 
+  // Because we are setting only an icon, let the inner button be labeled by us, so the accessible label can be overridden
+  gtk_accessible_update_relation (GTK_ACCESSIBLE (menu_button->button), GTK_ACCESSIBLE_RELATION_LABELLED_BY, menu_button, NULL, -1);
+
   image_widget = g_object_new (GTK_TYPE_IMAGE,
                                "accessible-role", GTK_ACCESSIBLE_ROLE_PRESENTATION,
                                "icon-name", icon_name,
@@ -1149,6 +1156,9 @@ gtk_menu_button_set_label (GtkMenuButton *menu_button,
   gtk_button_set_child (GTK_BUTTON (menu_button->button), box);
   menu_button->label_widget = label_widget;
 
+  // When the user explicitly set a label assume that it should be announced by assistive technologies as well
+  gtk_accessible_update_relation (GTK_ACCESSIBLE (menu_button->button), GTK_ACCESSIBLE_RELATION_LABELLED_BY, menu_button->label_widget, NULL, -1);
+
   menu_button->image_widget = NULL;
   menu_button->child = NULL;