Baup has been given a two-year deal with the club who finished 10th in Ligue 1 last season.
Baup, 57, led Bordeaux to the French league title in 1999, coaching the Aquitaine side from 1998-2003.
He then coached St Etienne, Toulouse, and Nantes in Ligue 2 and was a television pundit for three years.
Deschamps left the club on Monday, a year before the end of his contract.
- Sports & Recreation