Galtier, who had a year left on his contract, joined Lille in 2017 after eight years at Saint-Etienne and guided them to their first top-flight title since 2011.
The 54-year-old was close to former owner and president Gerard Lopez, who left amid the club's financial difficulties last December.
"With Christophe, we knew each other before working together in Lille," Letang said on the club's website.
"There has always been a lot of respect between us and our relationship has grown even stronger during our collaboration over the past five months. I naturally tried to convince him, but I believe his decision was already made.
"All Lille residents will keep wonderful memories of his time at LOSC, with the crowning glory of this title of champion of France. We can only thank him for everything he has brought here."