Preheat oven to 350°F (180°C). Grease a 9x13-inch baking dish; set aside.
In a large bowl, whisk together condensed soups and milk.
Stir in cooked chicken; transfer chicken mixture to the prepared baking dish.
In a separate bowl, pour melted butter over the dry stuffing mix. Gently stir until all of the stuffing mix is coated with butter.
Sprinkle the buttered crumbs over the chicken mixture.
Cover the dish with foil. Bake, covered, at 350°F for about 20 minutes. Remove foil and bake for an additional 10-15 minutes, or until heated through and browned on top.