The Tunisian winger has joined the Ligue 1 side for an initial £6million which could rise to £9million with add-ons.
However, he fell out of favour under David Moyes and only played a part-time role as Sunderland were relegated the following season.
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Khazri spent the majority of last season on loan at Rennes, where he produced some eye-catching performances, including scoring nine goals.
Rennes had hoped to keep the player, but were beaten to his signing by Saint-Etienne.
Part of the fee Sunderland have received will go towards paying the remaining money owed to Khazri's former club Bordeaux.