Norwegian Solbakken, 44, has signed a contract, the length of which was not disclosed, which starts on July 1.
Terry Connor, who has been in charge since the sacking of Mick McCarthy in early February, will lead the team in Sunday's final Barclays Premier League game at Wigan before standing down.
Solbakken said: "I am delighted to be taking up the important challenge to manage Wolves. It's an exciting opportunity to manage a great club and I can't wait to get started."
Wolves were widely criticised for the decision to turn to Connor, who worked previously as McCarthy's assistant, with the decision failing to inspire improved results and relegation was confirmed last month.
But the club's chief executive Jez Moxey was pleased to have secured the signature of Solbakken.
He said: "Following talks with Stale Solbakken I am happy to confirm that he has agreed to become our new manager. He will be formally introduced to the media on Monday."
Source: PA
Source: PA