Adams has also worked at Fulham and Leicester and was most recently assistant boss at Colchester.
Adams said: "Having worked at the club previously, which was a fantastic and rewarding experience, to get the chance to manage a super football club like Brighton & Hove Albion again was an opportunity I couldn't turn down.
"I look forward to working alongside Dean Wilkins, the players and the rest of the coaching staff - and working together with the Albion supporters - to try and get this club back into the Championship as we move towards our new home."
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