The former Charlton, Southampton and Newcastle manager took the Eagles to their first FA Cup final in 21 years last May, but has overseen a dramatic slump in the club's league form in 2016.
Palace have lost 22 games this calendar year and won just six times, leading to the one-time England candidate's dismissal.
Chairman Steve Parish thanked Pardew, who signed a three-and-a-half year deal in January after replacing Neil Warnock, for his service as both manager and as a player in the late 1980s and early '90s.
“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," he said.
"Following a fantastic second half of 2014/15, the 2015/16 season culminated in only narrowly missing out on winning the FA cup as well as securing our Premier League place for a record breaking fourth time. During his tenure Alan’s hard work and dedication were without question, he has improved so many areas of the club and we wish him the very best for the future.
"With games now coming thick and fast over the holiday period the club are hoping to put someone in place as quickly as possible but have nothing to say about a replacement at this time."
Pardew thanked Parish in return and said he continued to hold the club in special esteem.
"I would just like to take the opportunity to thank everybody at Crystal Palace for their fantastic support," he said.
"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."