The German bid farewell to his team-mates on Sunday and is expected to travel to Turkey today to complete his move to the Istanbul-based club.
Arsenal agreed to terminate Ozil's £350,000-per-week contract earlier this week to allow him to leave the club this month, rather than in the summer when his deal expired.
The paperwork for 32-year-old's move to Fenerbache is expected to be signed in the coming days, but an official announcement isn't expected until everything is completed.
Ozil leaves Arsenal after almost eight years at the club, having made 254 appearances and scored 44 goals, helping the club to three FA Cup triumphs.