Slice the bananas into thin rounds and cut the fresh pineapple into small, uniform chunks.
Place the prepared pineapple, banana slices, and entire contents of the mandarin orange can—including the syrup—into a large mixing bowl.
Sprinkle the dry vanilla pudding powder over the fruit mixture. Do not add milk or any additional liquids.
Using a spatula or large spoon, gently fold the ingredients together until the pudding mix fully coats the fruit and the salad takes on a creamy consistency.
Cover the bowl with plastic wrap or a lid, and transfer to the refrigerator to chill for a minimum of 1 hour before serving. Serve cold.