The England international completed the move on transfer deadline day to end a summer of speculation over his future.
The 29-year-old had failed to establish himself at Anfield since arriving on a free transfer last summer and had fallen well down manager Kenny Dalglish's pecking order.
Cole will get the chance to play UEFA Champions League football with the Ligue 1 club this season.
"I wanted a challenge from abroad," he said. "Lille is a beautiful club, a family club that plays well.
"I like intelligence in football. It will be an interesting experience for me.
"I think I'm going in the right direction. I'm here to help Lille by bringing my experience and the quality to win many trophies."