In a club statement, Palace chairman, Steve Parish said: “I would like to put on record our sincere gratitude for the tremendous service Alan has given us, both in his time here as manager and previously as a player.”
Palace have struggled this season and are currently 17th, having lost eight of their last 10 Premier League matches.
As to a replacement, Parish added that the club “are hoping to put someone in place as quickly as possible”.
Palace are next in action on Boxing Day, away to Watford.
In a brief statement on the Palace website, Pardew said: “I would just like to take the opportunity to thank everybody at Crystal Palace for their fantastic support. In particular a big thanks to the players who gave me absolutely everything and Steve Parish and his Board.
“Personally I have a lot of good feelings for this football Club and am sad that my time there has ended.
“I feel that I have a special bond with the club and hope that hasn’t been affected, I wish everybody associated with the Club the best of luck in the future including of course the fans who have been magnificent.
“There will be no further comment at the present time.”