He eats large quantities of fresh fruit and vegetables every day. He is after all a doctor, and knows the value of a good diet.
Also, McCoy lives in the 23rd-24th centuries, a period when medical technology is FAR ahead of what we have today. Today, if an old person is close to death because of a disease, many times it's considered not worth it to treat them because their bodies may not be strong enough to handle the treatment and recover, and because their life is expected to not last much longer anyway. In the Star Trek world, it's probably much easier to treat such conditions and to keep the body in good physical conditions. For that reason alone, life expectancy would probably go up exponentially.
On top of that, it's quite possible that in Star Trek they have some sort of cellular regeneration technique that lengthens human lifespan. Even today, scientists are working on many ways to lengthen the natural span of a human life and have had some success with animal tests.
In the post-DS9 novel series, it's implied that this is the case, as Vaughn is an old man (almost 150) and Picard remarks that he has decades ahead of him.