The 17-year-old had attracted attention from a number of clubs but has been signed 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 with the Seagulls before turning professional when he moves along the south coast.
"It's a great opportunity for me," the youngster told his new club'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."
Brighton goalkeeping coach Andy Beasley added: "I'm delighted to get him signed up. The scouting system did a great job in highlighting him so I went to watch him and straight away I was impressed by him.
"His mannerisms and the way he played the game just showed his potential. We're looking at all sorts of things. His handling and kicking is very good but the thing that really stood out to me was the way he trained and warmed up ahead of a game.
"You could see how professional he already was as a young lad and then he produced in a game and that's what you want to see in a young boy. He is dedicated to making himself right to play in the game.
"Bringing players in like Christian gives you that bit of excitement and you want to see him grow. He's very level headed and I'm looking forward to seeing him flourish."