The npower Championship club have moved quickly to replace Stale Solbakken after the Norwegian's ill-fated reign came to an end with a 1-0 defeat to non-league Luton in the FA Cup on Saturday.
Saunders began his management career with Wrexham in the Blue Square Bet Premier before taking over at Doncaster. A statement on Wolves' official website read: "Wolves are delighted to confirm that Dean Saunders is to become the club's new manager.
"Compensation has been agreed with Doncaster Rovers to allow the 48-year-old to take over at Molineux following Saturday's departure of Stale Solbakken."
The Welshman leaves Rovers, joint-top of League One, to join a club 18th in the Championship, six points above the bottom four. Solbakken managed just nine wins from 26 league games and the final straw came at Kenilworth Road as Wolves lost to a side 60 places below them.
Saunders' playing career included spells with Liverpool and Aston Villa, where he won the FA Cup and League Cup respectively, while he also earned 75 caps for Wales.
He left Wrexham after three years in charge at the Racecourse Ground, having guided them to the play-offs in 2010/11. When he departed, the Red Dragons were top of the table.
Despite relegation in his first season in charge at Doncaster, a colourful campaign which saw Rovers take a number of high-profile players on loan from agent Willie McKay's stable, Saunders has spearheaded a revival at the Keepmoat Stadium, with Rovers having taken 50 points from their 26 games.
A statement from Doncaster chief executive Gareth Baldwin published on the club's official site said: "We have agreed a good deal for Doncaster Rovers.
"Work has already started on trying to find a replacement for Dean and continue our push for promotion back to the Championship. 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."