Eight players have been released in all, with Adam Davies, Arron Jameson, Anthony Gardner, Miguel Llera, Martin Taylor and David Prutton joining the Johnsons in leaving Hillsborough.
Head coach Stuart Gray is to hold talks with the representatives of Chris Kirkland and Jose Semedo about new contracts at the club.
He also hopes to extend the deals of defenders Glenn Loovens and Oguchi Onyewu who only joined the club on short-term deals late in the season.
Five loan players have each returned to their parent clubs – Damian Martinez, Sam Hutchinson, Benik Afobe, Leon Best and Andelko Savic.
Gray said: “These decisions are never easy but they are part and parcel of football.
“There is no sleight on the players I will be letting go because they are great professionals who have always gone about their business in the right and thoroughly professional manner.
“But every manager in the country has his own ideas over how he wants his squad to look moving forward and I am no different.
“I am sure the released players will have no problem whatsoever in gaining new clubs. I would like to thank them all for their support and service to Sheffield Wednesday and wish them the very best of luck for the future.”