The Spanish right-back, 35, was an ever-present in the league last season and takes over from Gordon Greer.
"Bruno is hugely respected by everyone in the squad, throughout the club, and by the fans," manager Chris Hughton told the Seagulls' website.
"He's a fantastic professional and sets a superb example on and off the pitch. He stood in for Gordon Greer last season and he was the obvious choice."
Bruno was signed by Albion in 2012 after leaving Valencia and has made 148 appearances for the Sussex club.
"I'm really proud and it's a big responsibility for me," he said.
"It's about being an example for the young lads and the rest of the players."
Bruno has been installed as Brighton's captain for the coming season.