The current Seagulls boss Dean Wilkins has been offered the job of first-team coach at the Withdean Stadium, with the club hoping Adams can mastermind a promotion push next season.
Chairman Dick Knight told the club's official website: "This decision has not been taken lightly, but the board feel we need a manager with the wealth of experience to help the club make the leap into the Championship.
"Dean's strengths lie in coaching and the development of players and that is why we have offered him the role of senior coach under Micky."