The 62-year-old, who only took charge at Selhurst Park on December 23, guided the Eagles to safety on May 14 following a 4-0 defeat of Hull, who were relegated as a result.
However, the former England manager has now decided to walk away from his two-and-a-half-year deal with the south-London club following a meeting with chairman Steve Parish earlier on Tuesday.
“In some ways, this has been a very difficult decision to make, but in others it has been a simple one,” Allardyce said in a statement.
“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.”
The departure appears on amicable terms, with Allardyce’s stock again on a high following an impressive end to the domestic campaign.
‘’More than that (keeping Palace up), 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. As I said last weekend, Palace gave me the chance of rehabilitation,” Allardyce added.
‘’That’s why it’s hard walking away now. I believe the club are heading in the right direction with a hugely supportive board of directors, a great squad of players and some of the most passionate fans I’ve ever met. It’s been a privilege to have worked for them 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.”
There is reported to have been a break clause in his Palace contract which could be initiated following six months at the helm, and Allardyce is said to have been due a bonus in the region of some £2m for helping retain the Eagles’ top-flight status.
The Eagles struggled for consistency over the first part of the season under Alan Pardew, but eventually found form under Allardyce to pull clear of the relegation zone from the end of February with a run of six wins in eight games - which included wins at Chelsea, over Arsenal and away to Liverpool.
Despite losing 2-0 at Manchester United on the final day of the season, Palace ended the campaign in 14th place, some seven points clear of the drop zone.
Allardyce was expected to be busy in the summer transfer window, with the likes of rejuvenated England forward Jermain Defoe, who now appears set to join Bournemouth, on his radar.
However, the former England boss made it clear the decision was also a personal one and maintained he had “no ambitions to take another job”.
‘’I want to be able to savour life while I’m still relatively young and when I’m still relatively healthy, even if I’m beginning to feel all my 62 years,” he said.
‘’While I’ve got the energy, I want to travel and also spend more time with my family and grandchildren without the huge pressure that comes with being a football manager. I owe that to my wife and family.
"This is the right time for me, I know that in my heart. 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.
‘’Steve Parish has been superb during our conversations today. I know it came as a shock to him that I would walk away but our discussions have been incredibly civilised with no recriminations and no fall-out.
‘’This is not about transfer targets, club finances or anything along those lines. This is me taking the decision I believe is right for my family and myself. ’I would like to thank everybody for their messages of support since the news broke. I’ve no doubt I will miss management.’’
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