The Mali international had been on loan with the Championship club from French side Rennes since August of this year.
However, yesterday the 23-year-old agreed a deal with Wolves until the summer of 2016.
"I'm delighted we've signed him permanently and he can be an important player for Wolves for the next few years," said Solbakken. "We've already seen how quickly he's settled and what he can offer.
"I'm also confident when he gets even more used to the country and to his teammates, his game will grow even more and he'll get better and better."
Doumbia has become Solbakken's sixth permanent signing since he took charge of the club in May of this year.