Preheat your oven to 350°F (175°C).
In a medium saucepan, bring the chicken broth to a boil. Add the uncooked rice, cover, and reduce heat to low. Cook according to package instructions until the rice is fluffy and all the liquid is absorbed.
In a large mixing bowl, combine the cooked chicken, frozen broccoli, cooked rice, cream of chicken soup, milk, garlic powder, onion powder, and half of the cheddar and mozzarella cheeses. Season with salt and pepper to taste.
Stir the mixture until well combined.
Pour the mixture into the greased 9x13 inch baking dish. Spread it evenly.
Sprinkle the remaining cheddar and mozzarella cheeses on top of the casserole.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 15 minutes or until the cheese is bubbly and golden brown.
Remove from the oven and let it cool for a few minutes before serving.