The 21-year-old made his first-team debut for the Gunners during the 2020-21 season, and also penned a long-term contract.
Balogun featured in the Premier League just twice last season, before spending the second half of the campaign on loan at Middlesbrough - his first loan spell away from Arsenal.
While on Teesside, Balogun contributed three goals and three assists in 18 Championship appearances (nine starts) as Chris Wilder's team fell short of reaching the play-offs.
Reims finished 12th in Ligue 1 last season, 12 points above the relegation zone, and begins its new campaign on Monday (AEST) against Marseille.
Balogun becomes the French side's sixth signing of the transfer window, following the additions of Junya Ito, Andreaw Gravillon, Emmanuel Agbadou, Patrick Pentz and Maxime Busi.