Pepe was Arsenal's record signing when he joined from Lille for £72m in the summer of 2019. That fee has since been eclipsed by Declan Rice's arrival from West Ham United this summer.
The 28-year-old made 112 appearances for Arsenal and scored 27 goals but fell out of favour under Mikel Arteta and spent last season on loan at OGC Nice in Ligue 1.
Pepe was not part of Arteta's plans once again this season so a move away seemed to be the likeliest option despite having one year remaining on his contract at the Emirates Stadium.
Trabzonspor are seventh in the Turkish Super Lig and in a video posted on the club's Twitter account, Pepe said: "I came here to become a champion and achieve success."
Pepe has won 37 caps for the Ivory Coast national team, scoring 10 goals.
