You could try to engage your boyfriend in fun activities that also happen to be exercise.
Without knowing your boyfriend, it's hard to suggest something specific. Some examples are dancing, kayaking, playing squash, going on cycling trips or visiting places that require a lot of walking. Try picking something where exercise isn't the main goal. It's also important not to do anything very exhausting, because that might put him off quickly. Increase gradually, because to anyone who is not already into it, exercise seems like torture. If you get him to exercise more, you might find that he starts eating healthier as well.
Those suggestions come from my own experience. I started exercising, because I wanted to get fit for my outdoor trips, not because of the health benefits. While out hiking or cycling, I have had some of the most amazing experiences of my life and it's not possible to get there without a little training. When I'm in my training phase, I crave healthy food. I simply cannot ingest fast-food, because it seems revolting. Oh, when I'm not training, I actually like fast food quite a lot. In moderation, of course.
When exercising, I now take the yogic approach - do only what feels good. Do any more and you are overdoing it. If you still feel awesome after exercise(as opposed to spent), you are more likely do return to it the following day.
Gosh, thinking about how little fun I would have, if I wasn't reasonably fit, makes my heart shudder. Already looking forward to windsurfing in two weeks time.