He has been replaced by former Eintracht Frankfurt coach Oliver Glasner.
The 49-year-old Austrian signed a contract to the end of the 2025/26 season.
The changing of the guard came hours before Palace - who have won just twice in 14 League games - played out a 1-1 EPL draw at Everton.
Assistant manager Paddy McCarthy and Hodgson's long-term right-hand man Ray Lewington led the team at Goodison Park.
The result left Palace five points clear of their opponents, who moved out of the relegation zone on goal difference.
Former Frankfurt coach Oliver Glasner has signed to Crystal Palace to the end of the 2025/26 season. (EPA PHOTO)
A Palace statement said their former England manager was "out of hospital and doing well".
It was widely reported Hodgson was on the brink of being sacked when he was taken ill last week.
"I understand, given recent circumstances, it may be prudent at this time for the club to plan ahead," Hodgson said in a statement released by Palace.
"I have taken the decision to step aside so that the club can bring forward their plans for a new manager, as intended for this summer."
Hodgson was in his second spell in charge of Palace, having returned in March last year having been manager from September 2017 to May 2021.
He previously managed many clubs and national teams across Europe and beyond in a 48-year coaching career that took in Liverpool, Switzerland, Inter Milan, Finland and Fulham.
Glasner coached Eintracht Frankfurt for two seasons, leading the Bundesliga club to a Europa League triumph in 2022 and the German Cup final in 2023. He was previously at Wolfsburg.
"I'm delighted to welcome Oliver to the club," Palace chairman Steve Parish said.
"He has an outstanding record, and we believe he is the right manager to take the club forward at this pivotal stage."
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