The 29-year-old travelled to France on Tuesday to undergo a medical and, despite a late bid by Aston Villa, the player has opted to join the Ligue 1 club.
The England midfielder has failed to impress at Anfield having moved on a free transfer from Chelsea last summer.
His high wages - reported to be £90,000 a week - in relation to his diminishing role on the pitch meant Cole was identified as one of the players who manager Kenny Dalglish would be willing to let go in the current transfer window.
Cole has not featured in the squad for any of Liverpool’s four competitive matches so far and opted for a move to France after being attracted by the French club’s Champions League status this season.
It was reported in France that Lille were prepared to allow Cole to continue living in England and commute the 90-minute journey from London to France by Eurostar, although it remains to be seen whether that will be an option.
“With the arrival of England international Joe Cole, LOSC has clearly added to its squad both in quantity and quality," said Lille in a statement.
“The club is pleased and proud that the challenges facing us and our project has attracted a player of this magnitude.”