The Gunners signed the Ivory Coast winger in 2019 with much fanfare, agreeing to pay £72million over installments when he joined from Lille - a fee of which over £10m is still reportedly owed.
Pepe, 28, joins Turkish club Trabzonspor after his Arsenal contract ended a year before its expiration.
Arsenal said in a statement: “We can confirm that Nicolas Pepe is leaving the club. We have agreed with Nicolas to terminate his contract with immediate effect.
“Everyone at Arsenal thanks Nicolas for his contribution during his time with us and wish him well for the future.”
The player scored 27 goals in 112 appearances having spent last season on loan back in Ligue 1 with Nice. His last appearance for Arsenal came in October 2021.
Pepe becomes the latest player to have his contract terminated during Mikel Arteta’s reign in north London, following the exits of Mesut Ozil, Pierre-Emerick Aubameyang, Henrikh Mkhitaryan, Sokratis Papastathopoulos, Shkodran Mustafi, Sead Kolasinac, Willian and Hector Bellerin.