Pardew was confirmed as the new manager of Crystal Palace on Saturday, signing a three-and-a-half-year deal after Newcastle agreed to release him from his contract having agreed compensation with the Selhurst Park club.
John Carver and Steve Stone will remain in caretaker charge of Newcastle for Saturday's FA Cup tie with Leicester City, but a statement announcing Pardew's exit confirmed "the search for a head coach has begun".
Managing director Lee Charnley paid tribute to Pardew's efforts during his four-year stint at St James' Park.
"Despite public perceptions, fuelled by the media, Mike Ashley had never met nor spoken to Alan before his appointment. However, what developed over the last four years was a very strong and positive relationship between all parties," Charnley told Newcastle's official website.
"It is these relationships that, four years later, means the club is in a far better position, both on and off the field, and Alan has had a big part to play in that.
"During his time with us, Alan achieved two top-ten Premier League finishes, including a fifth-place finish in 2012, as well as taking us to the quarter-final of the Europa League. He goes with our best wishes and thanks."
Pardew added: "It has been a privilege to manage Newcastle United and I want to thank my captain Fabricio Coloccini and all the players, John Carver, Steve Stone, Andy Woodman and all the staff, all of who have been outstanding servants to Newcastle United.
"A special thanks also goes to the fans for all their support over the last four years. I must also thank Mike Ashley and the board for their unwavering support during my tenure at the club."
Pardew is set to come up against his former club on February 11 when Newcastle visit Selhurst Park for a Premier League fixture.
