The former captain was not in Brian Laws' plans for the forthcoming season and his deal, which had one year to run, has been cancelled by mutual consent.
Coughan was disappointed that he was not part of the manager's team for the 2007/08 season and finished on loan at Burnley towards the end of the last campaign.
The lion-hearted defended endured a torrid time last season with the untimely loss of his younger brother and was shipped out to Turf Moor to concentrate on football again following the good form of Richard Wood and Lee Bullen.
The former Plymouth defender scored 6 goals in 52 starts for The Owls and his presence on and off the pitch will be missed sorely by Wednesdayites.
In other news, Rocky Lekaj has signed his first professional deal at Hillsborough - penning a three-year agreement while young midfielder Sean McAllister has extended his current contract by a year.