The 62-year-old former England manager, said he had “no ambitions to take another job”.
Allardyce, who was in charge of the national team for just one match, took over at Palace from Alan Pardew in December on a two-and-a-half year deal.
He guided Palace to eight wins in 21 games. They finished 14th in the league.
“I will always be grateful to Crystal Palace and Steve Parish for giving me the opportunity to go out with my head held high having helped keep the club in the Premier League,” Allardyce said in a statement. "More than that, they gave me a chance of rebuilding my reputation after what happened with England.
Allardyce was sacked as England manager following a newspaper sting. His reign lasted just 67 days and took in one away game.
"I felt I needed another shot at being a Premier League manager and showing that I still had the ability to achieve something significant," the statement said. "As I said last weekend, Palace gave me the chance of rehabilitation."
Prior to becoming England’s manager, Allardyce was in charge of Bolton, West Ham, Newcastle and Sunderland.