Hyypia takes over from Oscar Garcia, who resigned as Seagulls head coach following the defeat by Derby in the Championship play-off semi-finals.
The ex-Finland international, 40, was sacked by German Bundesliga side Bayer Leverkusen in April.
"Brighton are an ambitious club and I am very pleased to have been given this opportunity," Hyypia said.
"I have looked at the club from top to bottom and I am very impressed by what I've seen at all levels."
Hyypia retired from from playing in 2011 at the age of 37 after spending the majority of his career at Liverpool where he won a Champions League medal amongst his trophy haul.