The 21-year-old is flying to England on Monday afternoon ahead of undergoing a medical on Tuesday before completing his big-money move.
Personal terms have been agreed with the player after Wolves and Milan thrashed out a deal.
Cutrone left Milan's USA tour late last week to travel home before heading to England on Monday.
It's believed Wolves will pay £16million up front for the 6ft striker, plus £4m in add-ons over the coming years.
Cutrone scored 16 goals in 42 games in his breakthrough season in 2017/18 before netting nine in 43 last year.
He is seen as an ideal alternative to Raul Jimenez and Diogo Jota and is described as a classic number nine with a strong work ethic and good aerial ability.
Speaking in Milan earlier on Monday, Cutreone told Calciomercato.com: "Reading all the messages from the fans made me emotional. It means that I’ve done a good thing.
“Am I disappointed? Well you have seen yourselves, I have nothing to say. I am always ready and charged. I wish the best for Milan fans and my teammates.
"My departure from Milan affects me as well but that’s life and some decisions are taken. I will look to do my best. Now I only think about integrating well and doing well there (at Wolves).
"I’m ready and excited to join Wolverhampton. It’s a big challenge for me."