The 24-year-old made only nine appearances for the club since joining in January 2008 and his contract has been terminated by mutual consent.
Grimsby are reported to be interested in Sweeney after his loan spell with the League Two club last season.
Simon Grayson said: "Sweens is at the stage of his career where he needs to play regular football and I can't guarantee him that here. He goes with our best wishes."