The 33-year-old has joined on a free transfer after leaving Palace, signing a two-year deal.
“Jason David Ian Puncheon – brilliant also on both wings of the attack,” a club statement read.
“This is one of the most important transfers in Cypriot football.”
Puncheon, who spent the second half of last season on loan at Huddersfield from Palace, added: “I am honoured to be joining Pafos FC.
“I believe the club has big potential and I am happy to become a part of the team and will work hard to bring Pafos to new successes.”