Solbakken – whose ill-fated spell at Molineux lasted from July 2012 until January 2013 – has agreed a four-year deal.
He replaces Lars Lagerback, who leaves by mutual consent after three years in the role.
“I am proud and honoured to have been offered the job as the new national team manager. For me, this is a good time to take over," said Solbakken, who played 58 times for Norway.
"Lars Lagerback and (assistant) Per Joar Hansen have done a solid job and developed a foundation that will be exciting to work on."
After being sacked by Wolves, Solbakken returned to Copenhagen where he won three Danish titles and three Danish cups before being relieved of his duties in October.
“Stale has a great coaching capacity and he knows Norwegian football very well," said Norwegian Football Federation president Terje Svendsen.
"He has good coaching experience, and he has delivered strong performances internationally for many years."