Spray a deep 9x13-inch baking dish with cooking spray.
Lay bread pieces into bottom of the prepared baking dish.
Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Spread sausage over bread.
Whisk eggs, cream of celery soup, and milk together in a bowl until mixture is smooth. Spread 1 package of Cheddar cheese over sausage; pour egg mixture over the cheese. Spread remaining package of Cheddar cheese over the top of the casserole. Cover with foil and refrigerate overnight.
Preheat oven to 350 degrees F (175 degrees C).
Bake casserole in the preheated oven until set, about 45 minutes; remove foil covering and continue baking until cheese topping is browned, about 15 more minutes. Let casserole stand 10 minutes before serving.