During two spells at the club, he managed 200 games across six seasons in total.
The 76-year-old had guided the Eagles to an 11th-place finish last term after taking over in March 2023 but has struggled to recapture that form this time around.
He leaves with Palace just five points above the relegation zone.
Hodgson said: “This club is very special and means so much to me and has played a big part in my footballing life. I have fully enjoyed my time here across six seasons, as it has given me the chance to work with top class players and staff doing what I love every day.
“However, I understand, given recent circumstances, it may be prudent at this time for the club to plan ahead, and therefore 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.
“I am confident that the season will finish well and I wish the team every success in the weeks, months and seasons to come.”
Chairman Steve Parish was also keen to praise the manager, commending his service to the London club.
“Roy has a special place in Crystal Palace history and this will never be forgotten. After four years in which he led the club to maintaining Premier League status season after season, he once again joined us nearly a year ago to steady the ship, and worked wonders," Parish said.
"That he then agreed to continue in the summer speaks volumes about his commitment to our club. Quite simply, we owe our continued Premier League status to Roy.
“I would like to thank Roy enormously for his service and wish him the very best for the future; it’s fair to say Roy has the keys to Selhurst Park and will always be welcomed back."
Hodgson fell ill during training on Thursday, February 15th and was taken to hospital, but it has since been announced by the club that he is in a stable condition and is doing well following his return home.
Former Frankfurt boss Oliver Glasner has since been appointed the new manager at Selhurst Park.
The Eagles are in action against Everton on Monday evening, with coaches Ray Lewington and Paddy McCarthy set to take charge.
