'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.'
Palace added: '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.'
In a 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.'
Pardew's last game as Palace boss was a 1-0 defeat by Chelsea at Selhurst Park on Saturday.
Palace had won one of their last 11 in the Premier League and only six times from 36 league matches overall in 2016.
Pardew leaves after overseeing 73 matches, winning 25 with a win percentage of 34 per cent. He drew 13 and lost 35.
He led them to 15th in the Premier League last season and to the FA Cup final, where they were beaten 2-1 by Manchester United.
Palace's next match is away to Watford on Boxing Day.