Preheat the oven to 350 degrees F (175 degrees C).
Place chicken into a pot and cover with water. Bring to a boil over high heat; reduce heat and simmer until no longer pink in the centers and juices run clear, about 15 minutes.
At the same time, bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain.
Drain cooked chicken and cut into bite-size pieces.
Place chicken, noodles, Alfredo sauce, ½ mozzarella cheese, milk, onion powder, and garlic powder in a large bowl and mix well.
Pour into a 1 ½-quart casserole dish. Layer remaining mozzarella cheese and Cheddar cheese on top.
Bake in the preheated oven until melted and bubbly, about 25 minutes.
