The 40-year-old, who was goalkeeping coach at Charlton last season, replaces Antti Niemi, who has returned to Finland for family reasons after just one season with the Sky Bet Championship club.
Albion manager Chris Hughton said: “We had a lot of very high-calibre applicants for the job, but Ben stood out as our number one choice. His credentials are first class, and he already has an understanding of the club.
“I’m delighted to welcome him to the club and am looking forward to working with Ben.”
Roberts, who helped Brighton win promotion to the Championship in 2004 as well as playing for Middlesbrough and Charlton, said: “I’m ecstatic to be back at Brighton. I’ve made no secret that my happiest years as a professional footballer were spent down here, as I had a special affinity with the fans at Withdean.
“I can’t wait to get started working with David Stockdale, Casper Ankergren and Christian Walton and I am very much looking forward to the season ahead.”