The two clubs were on Friday morning finalising the terms of a deal as Pepe’s disappointing spell in north London comes to an end.
The Ivory Coast international has one year left on his contract at Arsenal and is not part of manager Mikel Arteta’s plans.
Pepe spent last season on loan at French club Nice and the Gunners have been looking to offload him all summer.
He was unable to find a move before the transfer window shut across much of Europe on September 1, but has been given a lifeline by the Turkish window remaining open until next week.
Pepe has now flown out to Trabzon and filmed a video during the flight wearing the club’s shirt.
“I came here to become a champion and achieve success,” he said.
Bordo-Mavi formasıyla Nicolas Pepe geliyor pic.twitter.com/CG5Q3nhvUG
— Trabzonspor (@Trabzonspor) September 7, 2023
Pepe, who joined Arsenal from Lille in 2019 for a then club-record fee of £72million, is due to undergo a medical with Trabzonspor on Friday.
The player made 112 total appearances for the Gunners in four years across all competitions, scoring 27 goals.