In a large pot, heat the olive oil over medium heat. Add the cooked, shredded chicken and sauté for 2-3 minutes until heated through.
Stir in the BBQ sauce, garlic powder, onion powder, black pepper, and salt. Mix well to coat the chicken evenly.
Pour in the chicken broth and bring to a boil. Once boiling, add the elbow macaroni and stir.
Reduce the heat to low, cover the pot, and simmer for 10-12 minutes, stirring occasionally, until the pasta is cooked and most of the liquid is absorbed.
Remove the pot from heat and stir in the cheddar and mozzarella cheeses until melted and creamy.
Serve immediately, garnished with chopped green onions.