The 34-year-old signed a one-year deal with the Wearside outfit over the summer but has been allowed to find another club following the arrival of Danny Graham
The Frenchman moved to the Stadium of Light on a one-year deal after leaving Tottenham in the summer, but failed to net in his 14 total appearances on Wearside.
The £5 million arrival of Danny Graham from Swansea on Thursday left the veteran striker surplus to requirements, and the Mackems have now decided to bring his contract to an early end.
Speaking to the club's official website, Sunderland chief executive Margaret Byrne said: "We wish Louis all the very best for the future and thank him for his contribution to Sunderland."
The former Fulham, Manchester United and Everton man is expected to pursue his career outside of Europe, with clubs in Brazil and MLS said to be showing an interest.