Button, 29, has joined Jason Steele as goalkeepers signed this summer by Seagulls boss Chris Hughton as competition for Mat Ryan.
The Tottenham youth product spent two seasons at Fulham and helped them gain promotion to the Premier League – but has now headed to the south coast.
On the deal, Hughton said: “We’re delighted to bring a goalkeeper of David’s experience to the club.
“He has a wealth of experience, having made over 300 appearances during his career so far, and I’m sure he will work well with Maty Ryan and Jason Steele.”
Meanwhile, Button himself claimed: “I couldn’t be happier to be here. I’m delighted and looking forward to the season ahead.
“I saw how well the team did last season during their first year in the Premier League and every time I saw them I was really impressed.
“I thought the whole side did really well whenever I saw them, and a lot of players had good seasons.”
Button finds himself in something of logjam for places though – with Steele, another goalkeeper signed this summer, and Ryan for company.
But the ex-Tottenham ace can't wait for the challenge, adding: “There’s a lot of competition in my position and I want to be a part of that.
“It’s something that’s brilliant as a player and at this level it’s normal.
"They’re [Ryan and Steele] both great goalkeepers and I’m looking forward to working with them and helping us all improve.
“Training will be a good chance to get to know the lads straight away. I’m told it’s a great bunch.”
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