In a small bowl, mix the tuna and mayonnaise until well combined. Divide the mixture evenly among the tortillas and spread it out, leaving about a ½-inch border around the edges.
Sprinkle the shredded cheese over each tortilla, followed by the chopped celery and chopped eggs.
Starting from one edge, roll each tortilla tightly into a log.
Wrap each roll in plastic wrap and refrigerate for at least 1 hour, or until ready to serve.
When ready, remove the rolls from the refrigerator, unwrap them, and slice into 1-inch pieces. Discard the ends that don’t have enough filling.
Arrange the pinwheels flat on a platter and serve.