Preheat the oven to 350°F (175°C).
Prepare the Chicken Rice-A-Roni according to the package instructions, including the seasoning packet and butter.
While the rice is cooking, steam the broccoli florets until tender but still crisp, about 4-5 minutes. Drain and set aside.
In a large mixing bowl, combine the cooked Rice-A-Roni, steamed broccoli, cooked chicken, cream of mushroom soup, sour cream, milk, chopped onion, garlic powder, black pepper, and salt. Stir until all ingredients are well mixed.
Transfer the mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the shredded cheddar and mozzarella cheeses evenly over the top of the casserole.
Bake uncovered in the preheated oven for 25-30 minutes, or until the cheese is melted and bubbly and the casserole is heated through.
Remove from oven and let the casserole rest for 5 minutes before serving.