Former Liverpool striker Saunders was appointed following the sacking of former Norway international Stale Solbakken who left Wolves on Saturday after the team slumped to a shock 1-0 defeat at minor league Luton Town in the FA Cup third round.
"I have just come off the phone with Wolverhampton Wanderers' chief executive Jez Moxey and can confirm that Dean Saunders has agreed to take over as manager at Molineux," 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."
He failed to keep them in the Championship in his first season in charge, but mounted a promotion challenge that left them level on points at the top of League One on his departure.
Wolves, relegated from the Premier League at the end of last season, lie 18th in the 24-team championship standings.