Grease a 9x13-inch baking dish with cooking spray. Set aside.

Wrap tortillas in paper towels moistened with water; cook in the microwave until soft, about 20 seconds.

Stir condensed soup, taco sauce, green chiles, and green onions together in a large bowl. Fold chicken into soup mixture.

Spread some chicken mixture onto each tortilla. Sprinkle each with some cheese and roll up tortilla around filling; place seam-side down in the prepared baking dish. Spread remaining chicken mixture over rolled tortillas, then sprinkle with remaining cheese.

Cover the baking dish with aluminum foil; refrigerate for at least 8 hours to overnight.

Remove the baking dish from the refrigerator and let sit at room temperature for 30 minutes.

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

Bake in the preheated oven for 30 minutes. Remove aluminum foil and continue baking until cheese begins to brown along the edges, about 15 minutes more.