Saunders, who left Doncaster to take up the post, replaces Stale Solbakken, who was fired by the Molineux club after just six months following Saturday’s FA Cup loss to non-league Luton Town.
A club statement read: “Compensation has been agreed with Doncaster to allow the 48-year-old to take over.”
Wolves are Saunders’s third club in less than 18 months, the Welshman having also managed non-league Wrexham from 2008 until September 2011.
Doncaster chief executive Gavin Baldwin said: “I have spoken with Dean to thank him for the fantastic job he has done here at Doncaster and wish him well for the future.”