Negotiations between the two sides took place over the weekend, with Balogun undergoing a medical in France in recent days.
He spent the second half of last season on loan at Middlesbrough, featuring 18 times in the Championship and scoring three goals.
The England Under-21 international was on the cusp of leaving Arsenal just over a year ago before signing a new long-term contract in April 2021.
Reims finished 12th in Ligue 1 last season.
Jesus’ ability and attitude is lifting everyone around him – there is a buzz about Arsenal
(Photo: David Price/Arsenal FC via Getty Images)