Wolves, relegated from the Premier League in 2012 after a three-season stay, are in the Championship (second tier) after briefly dropping to the third level of English football.
Morgan, who took over eight years ago for a nominal 10 pounds ($15.19) but has invested millions in the club and revamped the stadium, has stepped down from the board.
"After eight eventful and enjoyable years at the club, and after much thought, owner and chairman Steve Morgan has decided to put his 100 percent shareholding in the club up for sale," a Wolves statement said.
"While the process of finding a new owner is being undertaken it is very much business as usual for the head coach, players, staff and all other stakeholders involved with Wolves.
"Steve would like to relay to all concerned that his ongoing commitment and financial support to Wolves will continue until a new owner can be found."
Wolves, who dominated the English game in the 1950s when they won three titles, are 16th in the Championship.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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