In a medium bowl, mix tomatoes, cucumber, bell pepper, celery, red onion, cilantro, and mayonnaise.
Cover and chill vegetables until ready to use.
Just before serving, prepare the avocado and stir into vegetable mixture. Using a slotted spoon to drain off any liquid, equally split the mixture between the 4 tortillas, placing the vegetables just off-center.
Roll up and cut each burrito in half. Serve immediately.