The 29-year-old travelled to France on Tuesday to undergo a medical and, despite a late bid by Aston Villa, has opted to join the Ligue 1 side.England international Cole moved to Anfield in July 2010 on a four-year deal from Chelsea but made only 11 league starts for the Reds.
He has not featured at all for Kenny Dalglish's side this season.
Dalglish has strengthened his midfield over the summer with the additions of Jordan Henderson, Charlie Adam and Stewart Downing and the club were apparently keen to get Cole off their wage bill.
Queens Park Rangers and Tottenham Hotspur were also interested in signing the former West Ham player, but he instead chose Lille, who will be playing in the Champions League this season after winning their first French league title since 1954.
"It looks to me that the club is going in the right direction and I'm excited about coming here and helping them win some trophies," said Cole.
"I always wanted to go to play abroad. I love football, I love watching it, I love talking about it. This is a great experience and a challenge to play for a team who wants to progress. This seems a very positive place."
A statement on Lille's official website said: "With the arrival of England international Joe Cole, LOSC has clearly added to its squad both in quantity and quality.
"The club is pleased and proud that the challenges facing us and our project has attracted a player of this magnitude."
Lille turned to Cole after being rejected by Monaco's South Korea striker Chu Young-Park, who is set to complete a move to Arsenal.
The French champions also failed with a bid for Chelsea's Yossi Benayoun.
This summer they have lost two players to the Premier League, with midfielder Yohan Cabaye joining Newcastle and Ivory Coast forward Gervinho moving to Arsenal.
