Allardyce, 62, kept south London side Palace in the top flight after replacing the sacked Alan Pardew in December, when the club was in 17th place just one point above the relegation zone. He had signed a 2-1/2 year contract.
"It's been a privilege to have worked here for the past five months. But there comes a time when you have to take stock of what direction you want your life to take - and that's been the simple part for me," Allardyce said in a statement.
"This is the right time for me. I have no ambitions to take another job, I simply want to be able to enjoy all the things you cannot really enjoy with the 24/7 demands of managing any football club, let alone one in the Premier League."
The former Bolton Wanderers, Newcastle United, Blackburn Rovers, West Ham United and Sunderland boss took over at Palace having lost his job as England manager last September following a newspaper sting after just 67 days and one game in charge.
On Sunday Allardyce spoke about the need to bring in the right quality players after a season in which Palace survived thanks largely to a fine run in March and April, which included victories over champions Chelsea, Liverpool and Arsenal.
Palace lost four of their last five games but their Premier League status was secured with a 4-0 win over Hull City on the second-last weekend of the season and they finished in 14th place on 41 points -- seven clear of third-bottom Hull.
Allardyce told chairman Steve Parish he had decided to step down at a meeting in London on Tuesday. The club are now looking for an eighth manager in seven years with former defender Chris Coleman, the Wales manager, the early favourite to take over.
"In some ways, this has been a very difficult decision to make but in others it has been a simple one," Allardyce said in his statement reported by British media on Tuesday.
"I will always be grateful to Crystal Palace and (chairman) Steve Parish for giving me the opportunity to go out with my head held high having helped keep the club in the Premier League," he added.
"More than that, they gave me a chance of rebuilding my reputation after what happened with England. I felt I needed another shot at being a Premier League manager and showing that I still had the ability to achieve something significant."
(Writing by Ken Ferris; Additional reporting by Neil Robinson; Editing by Hugh Lawson/Greg Stutchbury)
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