The ex-Bayer Leverkusen coach, who left the BayArena in April following a poor run of form, replaces Oscar Garcia at the Amex Stadium.
Spaniard Garcia exited after Brighton's Championship play-off semi-final defeat to Derby County last month, and Hyypia - who made over 450 appearances for Liverpool during his playing career - is delighted to have been handed his first managerial position in English football.
"I am absolutely thrilled by this appointment; Brighton and Hove Albion are an ambitious club and I am very pleased to have been given this opportunity," the Finn told the club's official website.
"I've held extensive talks with the chairman Tony Bloom and chief executive Paul Barber. I have looked at the club from top to bottom and I am very impressed by what I've seen at all levels.
"I've seen the Amex Stadium and the club's new training ground and they are amongst the best I've seen anywhere in the world.
"The chairman is ambitious and for me that is absolutely key. I am now looking forward to the challenge ahead and our aim is to take the club forward to the next level."
Hyypia took over at Leverkusen jointly with fellow coach Sacha Lewandowski in May 2012 following the sacking of Robin Dutt before being given the job permanently before the start of last season.
Hyypia will announce his backroom staff prior to the new Championship campaign.
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