In a large skillet over medium heat, cook onion, celery and broccoli in butter for 5 minutes. Add soup and milk and heat thoroughly. Remove from heat, add cheese and stir until cheese has melted.
Spread cooked rice in a greased 8-inch square baking dish. Pour broccoli/cheese mixture over; do not stir.
Bake, uncovered, at 325*F (160*C) for 30 to 35 minutes, or until hot and bubbly.