The 17-year-old had attracted attention from a number of clubs but has been snapped up by Gus Poyet's side on a three-year deal that will start in the summer.
Walton was still a scholar at Argyle and will complete his apprenticeship under John Sheridan before turning professional when he moves along the south coast.
"It's a great opportunity for me," the youngster told Brighton's official website. "I just want to knuckle down, work hard and hopefully one day I will break into the first-team squad.
"I was at the Amex on Tuesday night to watch Brighton play Blackburn and I liked the way the team played, and with the training ground on the way it's a great opportunity for me.
"Tomasz Kuszczak is a great keeper and has a lot of experience so I'm looking forward to learning off him and the other senior keepers at the club."
Argyle will receive a fee for the goalkeeper, as well as further payments depending on how well he develops with the Championship side.