Cisse joined Kuban Krasnodar from QPR in July after the English club's relegation from the Premier League, but will return to Ligue 1 after terminating his contract with the Russian outfit.
The 32-year-old is set to put to pen to paper on an 18-month deal with the Corsican club, who are winless in their last four Ligue 1 games.
A statement on Bastia's official website read: "After termination of his contract with the Russian club Kuban Krasnodar on the eve of the opening of the winter transfer window, the Sporting Club Bastia is pleased to announce the arrival of Djibril Cisse.
"The French international striker will undergo a medical on Wednesday January 1 at 10:00am (local time) and will sign an 18-month contract."
Cisse - a UEFA Champions League winner with Liverpool who also enjoyed spells with Marseille, Panathinaikos and Lazio - made 25 appearances for Kuban, scoring five goals.
Bastia sit 13th in Ligue 1 ahead of the resumption of the season, which will see Frederic Hantz's men face Evian in the Coupe de France on January 5 before travelling to Valenciennes in the league six days later.
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