Manchester United have agreed to meet Cunha's £62.5m buyout clause in his Wolves contract.
It's understood Cunha has undergone a medical and agreed personal terms with United, having met with directors over the weekend.
The 26-year-old was pictured leaving the Lowry Hotel in Manchester on Sunday morning.
Cunha is now set to join up with Brazil for Carlo Ancelotti's first game in charge for Friday night's World Cup qualifier against Ecuador.
Transfer confirmed
United have today announced Cunha's signing.
In a statement, the club said: "Manchester United has reached agreement with Wolverhampton Wanderers for the signing of Matheus Cunha.
"The Brazilian forward’s signing is subject to visa and registration.
"The 26 year-old has 13 senior caps for Brazil, and, in his club career, has made 270 appearances and scored 72 goals in the English, Spanish, German and Swiss top flights.
"During two-and-a-half seasons at Wolves, Cunha has scored 33 goals in 92 appearances.
"Everyone at Manchester United looks forward to welcoming Matheus to Old Trafford."