A day after the move was revealed, Button said on Thursday it would be strange being a rival to Brawn after seven years with the team.
"I am actually earning less than I would have been at Brawn so it's not about the money and everybody involved knows that is not the case. It's because it's something new," Button told BBC Radio.
After a long spell with Brawn, Button said he was sad to leave the team but happy to join fellow British driver Hamilton, even though they will remain rivals.
"I knew it would be a challenge to go up against Lewis in his environment and my goal since I was eight years old was to win the world championship and I've done that now and I feel in need of something else, a new challenge," Button said.
"On the emotional side there was definitely a lot to think about but I thought the challenge of going up against Lewis in his environment would be very tough but very exciting. I know the environment in both areas and I know what I want to do and I want new challenges."
Button had won only one grand prix before he won the 2009 title in a Brawn car which used imaginative technology to open a big early lead in the points standings. He finished 11 points ahead of Red Bull's Sebastien Vettel of Germany.
"History would say Ferrari and McLaren would build a very competitive car but last season Brawn came out with a stunner, a car that was beyond belief for a lot of teams so you never really know," Button said.
"You are always taking a gamble choosing any team but I do know there will be four or five teams at the front being competitive and I'm in one of those teams."
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