Bring a pot of water to a boil. Cook green bell peppers in the boiling water until soft, 5 to 8 minutes; drain.
Cook ground beef in large skillet over medium-high heat, breaking into small pieces with a spatula as it cooks, until completely browned, 7 to 10 minutes. Drain and discard excess grease. Transfer beef to a large bowl.
Stir rice, celery, onion, and about half the tomato sauce with the ground beef; season with salt and pepper. Stuff cooked green peppers with the ground beef mixture.
Arrange stuffed peppers in a baking dish. Pour enough water into the baking dish to about 1-inch deep. Pour remainder of tomato sauce over the peppers.
Bake in preheated oven until heated through, about 30 minutes.