Button is Brighton's fifth signing of the summer, following in the footsteps of Florin Andone, Leon Balogun, Jason Steele and Bernardo, and Seagulls boss Chris Hughton has spoken highly of the experience the goalie will bring to the AMEX Stadium.
Hughton told the club's website: “We’re delighted to bring a goalkeeper of David’s experience to the club.
“With Christian Walton and Robert Sanchez going out on loan this season, we felt we needed someone to provide further competition for places in that area of the team.
“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.”
Button added: “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 [Mathew Ryan and Jason 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.”
Button is Brighton's second goalkeeper signing this window after Steele, who left League One side Sunderland following their relegation from the Championship.
Brighton confirmed their Premier League status for a second consecutive season with a 1-0 win against Manchester United back in May and they will be looking to improve upon their points tally of 40, which saw them finish 15th.
Button mainly shared goalkeeping duties at Fulham with Marcus Bettinelli last season and the Cottagers are yet to bring in a new shot stopper perhaps indicating the 26-year-old will remain the number one for the upcoming campaign.
Fulham have signed Maxime Le Marchand and Jean Michael Seri so far this summer, both from Nice, with the latter regarded as a real coup after Barcelona were linked with the Ivory Coast international earlier this year.