The 40-year-old goalkeeper, who left Middlesbrough to move to London on a free transfer in 2008, has made more than 500 Premier League appearances during his career.
Two other players released by the west London club are defender Chris Baird and midfielder Simon Davies.
The 31-year-old Baird signed from Southampton in 2007, the same year that Davies joined from Everton.
Others released are midfielder Giorgos Karagounis and striker Mladen Petric, both of whom only spent one season at the club.
Alex Smith, James Musa, Richard Peniket, Tom Donegan and Corey Gameiro - who are all development squad players - have also been shown the door by Fulham.