The Stevenage-born Formula 1 star put pen to paper on a three-year deal with the German team after stating that he needed a "new challenge".
"It's nice to be the one who's not in that position it usually is me," said Button. "We all move about, that is how Formula 1 is. You are either looking for another team to give you a better chance of winning or you are looking for a new challenge."
Hamilton is due to replace Michael Schumacher, who announced today that he will retire from Formula 1 for the second time in his career at the end of the season.