The 41-year-old, whose only previous coaching experience was alongside Carlo Ancelotti at Paris Saint-Germain, will be assisted by Didier Tholot.
The former France international, who served as an assistant to Carlo Ancelotti during the Italian's time in charge of Paris Saint-Germain, replaces Frederic Hantz at the helm of the Ligue 1 side.
"Bastia are pleased to announce that Claude Makelele will be trainer for the next two seasons," a statement on the club's official website read.
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"He will arrive in Bastia on Monday, when he will sign his contract before being presented to the press the following day at 11:00.
"The former PSG man will be assisted in his task by Didier Tholot. The great family of Sporting Club de Bastia welcomes them both."
Makelele established himself as one of the finest defensive midfielders of the modern era during a career that took in spells at European superpowers such as Real Madrid, Chelsea and PSG before retiring from the game in 2011.