Yes tomatoes as well as many other types of vegetables including cucumbers are safe for dogs to eat.
Just cut the tomato up before feeding it to your dog so the dog can easily chew up the tomato and digest it easier.
You can add some tomatoes to your dogs regular dog food or just feed the dog some sliced tomatoes as a good healthy snack.
My dog eats tomatoes and cucumbers with me every time I eat cucumbers and tomatoes myself and he loves them.
Just make sure you do not let the dog eat the tomato stem or unripe tomatoes as the stem and unripe tomatoes contain Solanine which is a substance found in the stem and leaves of the tomatoes which is toxic to dogs.
But if you don't feed the dog unripe tomatoes or the stem of the tomatoes nor the leaves of the tomatoes the ripe tomato itself is very safe for dogs to eat.