A statement on Bordeaux's official website confirmed the departure of the player
Reports in France claim he has signed a four-and-a-half year deal with the Premier League side.
The statement read: "The club has reached an agreement with Sunderland AFC for the transfer of Wahbi Khazri.
"The playmaker has a great opportunity with the English club, and he was therefore allowed to go to England to negotiate with them."
Black Cats boss Sam Allardyce turned his full attention to Khazri after admitting defeat in his battle to sign Andre Ayew from relegation rivals Swansea.
And he will consider the capture of Khazri a victory after reports this week that both Everton and Aston Villa were also tracking the player.
Source : PA