The ex-France international is poised to sign a two-year deal with the Corsica-based side in what will be his first managerial role.
"Bastia are pleased to announce that Claude Makelele will be trainer for the next two seasons," a statement read on the club's official website.
Makelele, 41, had enjoyed a three-year spell on the coaching staff of Paris Saint-Germain, who recently recorded back-to-back Ligue 1 titles.
Club president Nasser Al-Khelafi also released a statement: "On behalf of the whole Paris Saint-Germain family and myself, I would like to thank Claude for his important contribution to our team's brilliant results, both in France and in Europe.
"We are all conscious of his role he played alongside Laurent Blanc and Carlo Ancelotti in the remarkable progression of the team."
Bastia finished last season in 10th place.