The 32-year-old, who departed Nice in the summer, admitted his delight following the completion of the move.
"I said four months ago that I was waiting for the opportunity that would really excite me. Bastia is a well-supported club with a demanding fanbase," he told the club's official website.
"The objective is to keep Sporting moving forward after two great seasons. I'm a guy who loves a challenge."
Sable made three appearances for France Under-21s.