The 33-year-old Landreau, who has 11 caps with France, left Lille by mutual consent on December 6.
Bastia, who are 13th in the Ligue 1 standings going into the European winter break, said Landreau would be presented on December 31.
Landreau, who started his professional career at Nantes in 1996, is looking to beat former Monaco keeper Jean-Luc Ettori's record of 602 French league appearances.
Landreau has featured in 568 French league games.
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