Preheat the oven to 350 degrees F (175 degrees C).

Combine chicken, cream of celery soup, cream of chicken soup, enchilada sauce, diced tomatoes and green chiles, onion, garlic, chicken broth, chili powder, and cheese in a 5-quart pot. Cook over medium-high heat, stirring occasionally, until cheese is melted and ingredients are well combined.

Spread a thin layer of chicken mixture in the bottom of a 9x13-inch baking dish. Layer remaining chicken mixture and tortillas in the dish as you would lasagna. Bake in the preheated oven until bubbly and cheese is lightly browned, 45 minutes to 1 hour. Let stand for at least 10 minutes before serving.