Solbakken, 44, will take over from acting manager Terry Connor and will start officially on July 1, the club said in a short statement on their official website.
Solbakken said he was delighted, adding: "It's an exciting opportunity to manage a great club and I cannot wait to get started."
Connor has been in temporary charge since Mick McCarthy was sacked in February but Wolves failed to win a game under him and were relegated on April 22. He is expected to return to his former coaching role, but will take charge for their final game of the season against Wigan Athletic on Sunday.
Solbakken won 58 caps for Norway between 1994 and 2000 and briefly played in the Premier League with Wimbledon in the late 1990s. He retired as a player after suffering a heart attack in training in 2001.
He led FC Copenhagen to Danish league and cup titles during a five-year spell at the club and into the Champions League for the first time, but had less success at Cologne, where he was sacked in April a few weeks before they were relegated from the Bundesliga.
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