Marseille will pay the 28-year-old defender from the Ivory Coast's salary.
Additionally, the agreement includes a 6 million euro (£5.07 million) obligation to buy, which is contingent upon performances and the Ligue 1 club's Champions League qualification.
In 2016, Bailly moved to United for £30 million from Villarreal, although he had trouble breaking into the starting lineup.
He has only played in 45 Premier League games over the past five seasons due to injury.
Bailly has fallen further down the Old Trafford pecking order than Raphael Varane did last season and Lisandro Martinez this summer.