Greer, 35, played 234 times for the club, while Zamora, also 35, scored seven goals in 26 games this season.
Adam Chicksen, Inigo Calderon and Andrew Crofts will also leave the Amex when their deals expire this summer.
Right-back Bruno has agreed a one-year deal, while contracts have been offered to Casper Ankergren and Niki Maenpaa.
Calderon, 34, was the Sussex club’s longest-serving current player, having scored 19 goals in 232 appearances since his debut in January 2010, while Greer moved to Brighton in the summer of that year and helped the club win the League One title in 2010-11.
Former England international Zamora re-signed for the club last summer, having previously scored 83 goals for the club between 2000 and 2003.
Left-back Chicksen, 24, and midfielder Crofts, 31, spent time away from the Amex Stadium on loan this season.
Brighton finished third in the Championship table, and only missed out on automatic promotion to the Premier League on goal difference.