The 30-year-old midfielder left West Ham in October after a falling out with new manager Slaven Bilic and has now returned to Ligue 1 as a free agent.
Lille has completed the signing of former West Ham midfielder Morgan Amalfitano on a free transfer.
The 30-year-old was frozen out of the first team at Upton Park after a bust up with manager Slaven Bilic and his contract was terminated by mutual consent in October.
Aston Villa had been linked with the player's signature, but he has now agreed to a two-and-a-half-year deal at Stade Pierre-Mauroy.