Murray joined the Cherries for £4m last summer on August deadline day but was restricted to just seven starts.
He scored 56 goals in three and a half years with the Seagulls after joining from Rochdale, helping the club win the League One title in 2011.
"Everyone at the club, and the supporters, know what Glenn will offer us," said boss Chris Hughton.
"He is a proven goalscorer and an excellent addition to the squad."
The former Barrow, Carlisle, Stockport, Crystal Palace and Reading forward joins Steve Sidwell and Ben Hall as new arrivals for next season.
Find all the latest football transfers on our dedicated page.
Championship side Brighton have re-signed Bournemouth striker Glenn Murray on a season-long loan deal.