Best Answer - Chosen by Voters
The Championship goes to the driver that scores the most points. Button scored the most points. So unless there is some argument that because he drove a car that was extremely good at the start of the year and shouldn't get as many points for winning, then yes, he absolutely deserved to win!
Last year's Mclaren seems to have been a better car than the Ferrari, should FIA go back and award Hamilton only 8 points for each of his wins since he had a better car, and thus give the Championship to Felipe? Or maybe we should revisit Schumacher's wins since the Ferrari's car was so much better in those years (but give him a Championship for 2006 when he just missed out and it seems like the Renault was so much better)? The fact is, the car is always going to be part of the equation. But where many drivers have the equipment and fail to get it there, Button aided in developing a car that was capable of running away with it at the start of the season and then did just that. He scored the points, and deserved them.
As for the future? Button is an interesting driver to watch... a few races before he won for the first time a few year's ago I was convinced he'd never win a race. But once he did win, he seemed to suddenly show all the promise again. Which then slowly disappeared until the start of this season - the second part of the year being less spectacular, but he continually did what was needed to bring home the championship (something Lewis Hamilton couldn't do in his first try).
Button is a completely different driver when he is driving with confidence, and as he showed in Brazil, driving with a purpose. If next year's Brawn is competitive he will likely continue to be in the mix in the future (assuming he's at Brawn - though he will probably be there or at another competitive team). But another championship will prove elusive unless he can take the next step as a driver and begin to bridge that difference between the confident and nonconfident driver he's been in the past. If he continues to develop as a driver, and shows a talent for helping develop good cars (areas where champions like Schumacher and Alonso excelled), then he has a good chance of getting a second championship.
However, all things considered, it's probably most likely that he will wins some races, score a decent amount of points, and have a very solid career - but ultimately fall short of being at the very top again.