In a medium bowl, combine the shredded cooked chicken breast, mayonnaise, Greek yogurt, and Dijon mustard.
Mix well until all ingredients are evenly combined.
Add salt and black pepper to the chicken mixture and stir to incorporate.
Fold in the chopped celery, red bell pepper, cucumber, and red onion until evenly distributed.
Lay out the four slices of whole wheat bread on a clean surface.
Place a large lettuce leaf on two of the bread slices.
Spoon half of the chicken salad mixture evenly over the lettuce on each slice.
Top the chicken salad with two slices of tomato on each sandwich.
Cover each sandwich with the remaining bread slices to form two complete sandwiches.
Cut sandwiches in half if desired and serve immediately.