Well, if I hadn't heard his history of back pain, I would say he might just bucking out of pleasure. Once you get it cleared up completely by your vet and chiro, that is he is 100% sound, then start jumping again. If he is still bucking at landing, I would then check your riding. Maybe when your landing you are landing on his back to hard, causing pain, who knows. Check his teeth for any possible tooth problem. Last of all, it may just be pleasure bucks. But before you decide its simply pleasure bucks, rule out every other possibly out come.
Lots of horses do buck out of pleasure, actually. Its not a very un common thing. But dont rule out any possible pain issues causing this bucking :) He may seem eager, but many horses are very good about hiding pain.