The one-cap Italy international has left his boyhood club to take up a four-year contract at Molineux.
"I'm very pleased to be here because the club really wanted me. I'm very happy and want to give my all for the team," Cutrone said in a statement.
"The club really wanted me and being able to play in the Premier League for Wolves is fantastic. I just can't wait to get started.
"I've come here to play football. I'll have to settle in initially and I'm looking forward to heading out on to the pitch to play.
"You never stop learning and I'm here to learn new things, but I'll certainly give my all for the team."
Wolves sporting director Kevin Thelwell added: "Patrick is an exciting signing at a very exciting period for this football club.
"We have a strong philosophy under the leadership of Nuno [Espirito Santo] of bringing in the right type of people and developing young talent while staying humble and grounded as individuals, and we feel Patrick perfectly fits into our philosophy.
"We are very pleased to have a player of Patrick's ability join the club and look forward to him being a part of Nuno's squad in another historic season for Wolves."
Cutrone, 21, looked at home when he broke into Gennaro Gattuso's side two seasons ago, scoring 18 goals in all competitions.
Fewer starting chances resulted in a less prolific second campaign, although another four goals in Europe lifted his career tally on the continent to double figures.
That record could prove useful for Wolves as the Premier League club target a place in the Europa League group stage.
Nuno's men take a 2-0 advantage into the second leg of their qualifying tie against Northern Irish side Crusaders on Thursday.
Jesus Vallejo, who joined on loan from Real Madrid, is Wolves' only other new signing to date.
Milan, meanwhile, will likely have to pursue a replacement partner for Krzysztof Piatek in new boss Marco Giampaolo's preferred two-striker system.