The 33-year-old was officially unveiled by the Corsican club on Monday after signing from Lille.
His new club are 13th in Ligue 1, but Landreau, who has 11 caps for France, said he was made to feel at home in Bastia.
He told the club website: "I am happy to wear the Bastia colours. I was touched by the warm welcome at the airport.
"I could have joined Bologna or Inter Milan. My goals in life are more the things that can make me grow as an athlete and a man. That is my motivation."