The former Maccabi Tel Aviv boss and Barcelona youth-team coach replaces Gus Poyet and penned the deal on Friday.
The 40-year-old, who has appointed Juan Torrijo and Ruben Martinez into his backroom staff, believes he can take the Seagulls all the way.
"I am delighted to have signed a long-term contract with the club and I am now very much looking forward to the challenge ahead," he told the club's official website.
"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 have already received a very warm welcome from the club's staff, players and supporters.
"Brighton & 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 am looking forward to an exciting season."