The former Wales striker emerged on Sunday morning as the preferred candidate of Wanderers, who have moved quickly to replace Stale Solbakken who was sacked on Saturday night after a poor run of form.
In a statement on Sunday night, Doncaster's chief executive Gavin Baldwin confirmed the move.
"I have just come off the phone with Wolverhampton Wanderers' chief executive Jez Moxey, at 8.50pm Sunday evening, and can confirm that Dean Saunders has agreed to take over as manager at Molineux," he said on the club's official website.
"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."
The recruitment was acknowledged by both sides on Monday morning.
Wolves said on their official website: "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."
Saturday's FA Cup third-round defeat to Luton proved to be the final straw for a Wolves board who have watched Solbakken fail to get a side relegated from the Premier League last season back on track.
With just three wins in 16 they languish in 18th place in the Championship, with the club describing results as "hugely disappointing".
Solbakken, 44, joined the Midlands club last summer following his dismissal by German side Cologne, with the former Wimbledon midfielder - once pronounced clinically dead after suffering a heart attack in training which forced his retirement from playing - boasting five Danish titles won in charge of Copenhagen.
Saunders is Wolves' fourth boss in less than a year after the departure last February of Mick McCarthy and the brief tenure of Terry Connor.
A former Liverpool and Aston Villa player, Saunders got the Doncaster job after Sean O'Driscoll was sacked last season.
He presided over one of the most colourful periods in the club's history which saw them relegated to League One with a squad made up of loan signings, provided primarily by agent Willie Mackay.
The likes of El-Hadji Diouf and Pascal Chimbonda all turned out for Rovers but could not prevent relegation, although Saunders has enjoyed a better time of it this time around, with his team joint-top of League One.
Elsewhere in the Championship on Sunday, O'Driscoll, sacked by Nottingham Forest despite a Boxing Day win over Leeds, confirmed he had rejected the chance to take over at Barnsley.