The striker has scored a five-year contract until June 2028 to return to Ligue 1 after a stunning season with Reims, where he scored 21 goals.
Balogun joined the Gunners aged 10 and developed through the club's academy before signing a first professional contract in February 2019 and made his senior debut in the Europa League the following year.
In January 2022, Balogun joined Championship side Middlesbrough on loan where he netted just three times in 20 appearances.
A club statement from the Gunners read: "We thank Folarin for his contribution to Arsenal, through our Academy into the first team, and wish him the best of health and happiness in his new chapter at Monaco."
The Gunners are set to sanction exits for a number of other fringe players before Friday’s transfer deadline. Nuno Tavares is set to join Nottingham Forest in a deal worth £14m.