The Seagulls confirmed the departure of the Scot, who has previously managed Reading, Leicester, Wolves and Millwall.
The popular Jock had two spells at Newcastle. He signed from Morton in 1977 and spent a year at the club before returning to Scotland with Aberdeen. He won everthing in the game under Alex Ferguson, including the Cup Winners Cup, then joined Celtic.
He returned to St James' Park in 1989 then joined IK Braga two years later. In all he made 115 appearances for Newcastle, scoring 36 goals.
Brighton statement: "Mark understands that and has agreed to step down. A lot of people thought Mark would be leaving at the end of last season but at that time I backed him, I thought he needed the chance. What has happened is the fans have really got on Mark's back and that is the way it is in football, and the team needs to be rejuvenated."