Someone who is very into health and fitness is often called a fitness freak. This term can be somewhat derogatory: it may have negative implications that they are obsessed with their hobby, or that their emphasis on fitness is annoying to other people. It can also be used in a positive way too, though, and many people will positively identify as a "fitness freak". Here is an example of one negative and one positive use.
Back in college, my roommate and I were digging into some chips when my friend, a fitness freak, walked in and gasped, "Oh my gosh, I would never eat those." We looked at each other like we'd just discovered we were eating a handful of dog poop. Fitness freaks can make others feel bad about their choices by pointing out our perfection. — Paige Waehner, "10 Signs You Might be an Annoying Fitness Freak", about.com (8 July 2014)
You wouldn't think it if you saw his thin frame. But musician Dr Ricky Kej (more on the epithet later) is unmindful of healthy eating and exercise. "He's been a member of three gyms, but hasn't made use of it. He just can't live without fast food," says his self-proclaimed fitness freak wife Varsha, who, on the other hand, ensures to run six days a week. — Vidya Iyengar, "Together, despite the differences", Bangalore Mirror (19 October 2014)
That is very close to gym freak, though exercise is only one part of staying healthy. A more catch-all term is health and fitness fanatic. This suggests more of a health-centric lifestyle (though from my previous quotations you can see that "fitness freak" also extends into areas like diet). More fitness-specific is "fitness fanatic", which doesn't seem to have some of the negative overtones of "fitness freak".
There isn't much that phases Fred Turok. But when the compère for the Entrepreneur of the Year awards bash made a cheap joke at the expense of his broken leg, the hard-nut South African health and fitness fanatic was clearly ruffled. — Susie Mesure, "The fitness fanatic who aims to bulk up the health clubs sector", The Independent (12 August 2002)
On the personal fitness side, there are also gym bunny (often used for women or gay/feminine men, according to Wiktionary among other sources) and gym rat (Wiktionary definition) but these suggest a degree of obsession which may make them somewhat pejorative.