Go to a gym, spend less time sitting down, get a standing desk, that kinda thing.
(1) Exercise more. Many people have reported feeling a lot better once they just started exercising and strengthening up their muscles (back muscles in particular).
(2) Get a height-adjustable desk and spend part of the day standing.
I watched my dad suffer through severe back pain when I was younger. He had to have surgery twice. His was caused by football most likely, but still, what I can tell you is you don't want to let this grow into a legitimate back problem. I've witnessed the impact it can have. It's not something to be trifled with.
Also, set an alarm to get up from your desk once an hour. Just taking a trip to the bathroom or the water cooler will help keep you active enough.
[1] I do this routine a couple times a month: http://www.mayoclinic.com/health/back-pain/LB00001_D
(Building some lower-back strength with deadlifts would be the next step, but might be more than you need just to avoid pain.)
You should also try to get out of your chair and move about for a few minutes as often as possible throughout your day. Among other things, the slouching/hunching/shifting in your chair is often an attempt to alleviate the pressures placed on your spine while sitting. Forcing myself to get up with a timer made a huge difference with my back pain. Before, I was at my chiropractor's office at least once a week.