Gus Poyet led Albion to the Championship play-offs last season but he was sacked as boss on Sunday for an unspecified breach of discipline.
The Uruguayan claimed he was informed of the club's decision while working as a TV pundit for the Confederations Cup, although the club has denied this.
But Brighton have acted quickly to name his replacement, with 40-year-old former Barcelona, Valencia and Espanyol midfielder Garcia due to take over at the Amex Stadium.
Garcia led Tel Aviv to the Israeli Premier League title in 2012/13 and also assisted Johan Cruyff with the Catalonia national team.
Poyet is appealing his sacking, while assistant manager Mauricio Taricco is back at work after a suspension imposed on him was lifted.
Coach Charlie Oatway is still currently serving a club suspension.
Maccabi have already stated that their assistant coach Ruben Martinez and head fitness coach Juan Torrijo Navaro are leaving the club to join Garcia in his next role.