The Championship club have turned to Garcia, 40, to replace Gus Poyet after the Uruguayan was sacked as manager at the weekend.
Poyet is set to appeal against his dismissal but the Seagulls have handed Garcia the newly-created position of head coach, which he will begin on Thursday morning.
Garcia, who quit as Maccabi Tel Aviv boss last month, inherits a side which finished fourth in the Championship last season.
However, what appeared to be a successful campaign quickly unravelled following the play-off defeat by bitter rivals Crystal Palace.
Poyet - who hinted he was considering his future after the game - assistant Mauricio Taricco and coach Charlie Oatway were suspended last month pending an internal inquiry into alleged breaches of contract.
Following a disciplinary hearing, the former Chelsea and Tottenham star's dismissal was announced by Brighton while he was working as a pundit for the BBC on Sunday night.
Taricco had his ban lifted but left the club by mutual consent on Wednesday evening, while Oatway is still suspended.
Meanwhile, Maccabi have announced that assistant boss Ruben Martinez and fitness coach Juan Torrijo Navaro have left to "continue their partnership with Oscar Garcia".
Garcia played for Barca for six years and also coached the club's youth team before guiding Maccabi to the league title last season.