The 32-year-old has scored 16 goals in 169 appearances but struggled for game time under Roy Hodgson this season, and secured a January loan move to Huddersfield Town until the end of the campaign.
"It's been an honour and a privilege to have represented my hometown club and I leave with memories that will stay with me forever," Puncheon said.
"I would like to thank everyone at Palace; in particular all of my team mates and the managers and coaches I've played under."
Palace manager Hodgson hailed Puncheon and goalkeeper Julian Speroni, who will also leave, as professionals "worth their weight in gold".
"I was unlucky to lose Jason Puncheon for six months at that time but I've got to say both have been absolutely excellent as professionals and human beings," Hodgson told reporters.
"It's no surprise to me that they are so highly regarded, particularly by the fans. People that are prepared to shed blood almost for the jersey are worth their weight in gold."
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
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