The Championship side announced on Sunday night that a deal had been agreed with Saunders' previous club Doncaster and just the formalities remained to be completed.
And they have now released a Monday morning statement which 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.
"Saunders, who has completed the UEFA Pro Licence, has guided Rovers to second place in League One this season, having started his managerial career with Wrexham.
"He has also worked in the top flight as a first team coach at Blackburn and strikers coach at Newcastle, as well as being assistant manager of Wales for three years.
"Saunders enjoyed an illustrious career as a player, winning the FA Cup with Liverpool and League Cup with Aston Villa, and is also fourth on the all-time goalscoring list for Wales with 22 goals from 75 appearances."
Wolves have moved quickly to bring in Saunders, having fired Solbakken after a 1-0 FA Cup loss at Luton proved to be the climax of a disastrous six-month tenure which ended with Wolves 18th in the Championship and in the midst of a terrible run of form.
And Saunders said: "It was a very difficult decision to leave Doncaster but this is a big club, it's a big challenge, and I am looking forward to it.
"It is a tough league and we have to try and get up the other end of it. We have to hit the ground running.
"There are no secrets in football - it's about good players working hard and that is what I will be pointing at. It's a great club and I am proud to be the manager."