Lille chairman Michel Seydoux said in a press conference at the club's Camphin-en-Pévèle training ground on Wednesday that it was a "huge honour" to have such a talent join the club.
"It's rare in the history of football to see a transfer going in this direction across the Channel," he said.
A large number of French footballers currently play in the English Premier League including two players from Lille, Yohan Cabaye and Gervinho, who moved to play at Newcastle and Arsenal this summer.
Cole is the first player to move in the opposite direction since Trevor Steven left Rangers for Marseille in 1991.
The player told local newspaper La Voix du Nord that he had been wanting to play abroad for some time.
"I'm coming to a good club that plays great football and is very friendly," he told the newspaper. "I've been here since yesterday and everything is positive and the place itself is magnificent."
He praised the Lille team as a sort of "little Barça", a reference to current European and Spanish champions Barcelona, saying they "pass the ball quickly and well."
The move could give the 29-year-old more action on the pitch since his move to Liverpool on a free transfer from Chelsea last summer. He has had a difficult time at Liverpool's home in Anfield, battling with injury and only managing nine Premier League starts.
Another bonus for the midfielder could be Lille's closeness to Cole's native London. The travel time is just 1 hour and 20 minutes on the Eurostar.