The 40-year-old was sacked by German outfit Bayer Leverkeusen in April but will now embark on a managerial career in England after being named as Oscar Garcia's replacement.
Hyypia, who won two FA Cups and the Champions League in his 10 years and 464 games at Anfield, revealed he had taken an in-depth look at Brighton before deciding on accepting the position with the south coast side.
"I've held extensive talks with the chairman Tony Bloom and chief executive Paul Barber," he said.
"I have looked at the club from top to bottom and I am very impressed by what I've seen at all levels."
The Finnish star's sacking at Leverkusen came after a run of just one win in 12 matches.
The Seagulls were led into the play-offs by former manager Garcia, but for the second consecutive season they were beaten at the semi-final stage.
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- Oscar Garcia