The Sunderland manager was dismissed by the Sky Bet Championship side in June over an alleged incident of gross misconduct whilst in the care of his duties.
He appealed the decision to Brighton's board, but that was rejected, and he then took up the option to go down a legal route by taking the club to a tribunal.
But a statement made by a legal representative on behalf of Mr Poyet read: "In relation to Mr Gus Poyet's departure from Brighton Football Club, both Mr Gus Poyet and Brighton Football Club have now reached a settlement whereby Mr Gus Poyet has withdrawn his Employment Tribunal Claim.
"Mr Gus Poyet would like to take this opportunity to express his sincere thanks to Brighton Football Club and in particular the fans for the tremendous support received during his time as manager at Brighton Football Club.
"Mr Gus Poyet wishes both Brighton Football Club and the fans well for the future."
Poyet was appointed as Paolo Di Canio's replacement at the Stadium of Light in October, with his second game in charge seeing Sunderland beat Newcastle 2-1 in the Wear-Tyne derby.