Heat the olive oil in a large skillet over medium heat. Season the diced chicken with garlic powder, onion powder, Italian seasoning, salt, and pepper.
Cook the chicken for 6-8 minutes until golden and fully cooked. Remove from skillet and set aside.
In the same skillet, melt butter over medium heat. Sauté minced garlic for 1-2 minutes until fragrant. Whisk in the flour and cook for 1-2 minutes.
Gradually add milk, whisking constantly, and cook until the sauce thickens (3-4 minutes). Stir in mozzarella and cheddar cheese until smooth. Season with salt and pepper.
Preheat oven to 375°F (190°C).
Lay the tortillas flat and divide the cooked chicken evenly among them. Roll each tortilla tightly and place seam-side down in a baking dish.
Pour the creamy cheese sauce over the wraps, ensuring they are generously coated. Bake for 10-12 minutes until the cheese sauce is bubbly and slightly golden.
Garnish with additional shredded cheddar cheese, if desired. Allow to cool slightly before serving.