The 28-year-old, who will wear the No.16 shirt, arrives as a free agent following the termination of his deal with Lille.
Bodart has been brought in to provide cover after first-choice goalkeeper Lionel Mpasi suffered a serious injury.
The Seraing-born shot-stopper began his career at Standard Liege, making 190 professional appearances, keeping 47 clean sheets and conceding 262 goals.
He joined Metz in January 2025 and played a role in their promotion to Ligue 1 before moving to Lille last summer. However, Bodart struggled for regular opportunities, making only five appearances during the 2025-26 campaign.
A former Belgium Under-21 international, Bodart has yet to represent the senior team, although he has been named on the bench for the Red Devils six times.