Cunha is expected to pen a five-year contract with the Old Trafford club, who have the option of extending the deal by a further 12 months.
"Manchester United has reached agreement with Wolverhampton Wanderers for the signing of Matheus Cunha," a United statement said.
"Everyone at Manchester United looks forward to welcoming Matheus to Old Trafford."
The 26-year-old was in Manchester over the weekend to put the finishing touches to his move, which is subject to a visa and registration.
Cunha, who has won 13 caps for Brazil, scored 18 goals in all competitions for Wolves this season, winning the club's player of the year award.
The Brazilian finished his Wolves career with 33 goals in 92 appearances in all competitions after signing from Atletico Madrid in January 2023.
United activated the release clause in Cunha's Wolves contract to ensure he becomes boss Ruben Amorim's first signing of the summer transfer window.
Amorim's side lost the Europa League final against Tottenham to cap a dismal season featuring a 15th-place finish in the Premier League that ranked as their lowest final position since 1973/74.