Put the eggs in a large saucepan and pour in enough cold water to cover by 1-inch. Bring to a boil over high heat. Remove from the heat, cover, and set aside for 15 minutes. Transfer the eggs to a bowl of half ice and half water. Cool completely, then peel under cold running water.
Cut the eggs in half lengthwise and remove the yolks. Keep the halves of the whites intact. Place the yolks in a strainer set over a large bowl and force through with the back of a large spoon. Add the mayonnaise and stir until smooth.
Combine the tuna, anchovies, capers, lemon juice, and olive oil in a food processor. Process until smooth and creamy. Stir into the yolks and season with salt and pepper. Mound a heaping spoonful of the yolk mixture into the cavity of the whites. Garnish with a celery leaf and an olive. Keep chilled until ready to serve.