The England under-20 international linked up with his new team-mates on Tuesday after Bury returned from their pre-season tour.
Albion manager Chris Hughton said: “We want Christian to play regular first-team football as soon as possible and Bury will give him that opportunity.
“Bury are a club who have a similar playing philosophy to us, and in David Flitcroft I feel they have an excellent manager who will be good for Christian.
“They have just moved into Manchester City’s old training facility in Carrington and, having won promotion last season, Bury are a club with ambitions to continue their progress.
“They’re a good fit for Christian, he will get the opportunity to play regularly at a good level and I am confident this loan move will benefit all three parties – Christian, Bury and ourselves.”
Walton, 19, made three Championship appearances for the Seagulls last season after being handed his debut against Tottenham in the Capital One Cup.
Hughton has David Stockdale, Casper Ankergren and new signing Niki Maenpaa vying to be first-choice keeper next term.