Cole, 36, joined up with his former Manchester United team-mate Keane on a one-year deal last summer but only made five appearances for the Black Cats.
Former Leeds player Harte was also brought in by Keane, who he played alongside for the Republic of Ireland, in 2007.
Varga joined Sunderland from Celtic in 2006, while Wright joined from Liverpool in 2002 for �3m and recently had a spell on loan at Stoke.
Academy graduates Jack Pelter, Gavin Donoghue, Billy Dennehy and Jake Richardson have also been told they must find new clubs.
Veteran midfielder Dwight Yorke is still in negotiations over a new deal.
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