The Championship club announced on Friday night that Garcia had put pen to paper on his Albion contract earlier in the day.
The 40-year-old was initally appointed at the end of last month, but Brighton were forced to wait for the outcome of former manager Gus Poyet's appeal hearing before finalising details.
Garcia guided Maccabi Tel-Aviv to the Israeli Premier League title last season and has brought Juan Torrijo and Ruben Martinez with him to the Amex Stadium to be his assistant coaches.
In addition, Garcia has appointed former Brighton full-back Nathan Jones to the position of assistant head coach. Jones had previously held jobs at Yeovil and Charlton.
Speaking to the club's official website, Garcia said: "I'm delighted to have signed a long-term contract with the club and I'm now very much looking forward to the challenge ahead.
"Brighton is one of the most exciting clubs in Europe and the potential here is very good. The squad is strong and the footballing set-up is excellent. The aim is to continue the good progress that the club has made in recent seasons.
"I've already received a very warm welcome from the club's staff, players and supporters. Brighton and Hove is a very nice city, the stadium is superb, and a world-class training facility is being built for our use from next season.
"Pre-season preparations are going well and like the supporters, I'm looking forward to an exciting season."
Brighton begin their Sky Bet Football League Championship campaign with a tough fixture away to Leeds United on Saturday, August 3.