The Eagles have struggled this season, having finished 15th last term, and Pardew has now left Palace just three days before Christmas.
In a club statement issued on cpfc.co.uk, 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.
"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."
Pardew, who spent just over three years on Tyneside and was in charge when the Magpies finished fifth in the top flight in 2011/12, left Newcastle for Selhurst Park in January 2015.
He 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."