The 26-year-old exits Molineux in a club-record sale for Wolves after two-and-a-half seasons with the old gold.
Cunha leaves after 33 goals in 92 appearances for Wolves, having initially helped the club retain its top-flight status in his debut 2022/23 campaign, he shone the following season.
Cunha, who has 13 caps for Brazil, sees his transfer to the Old Trafford club subject to visa and registration formalities.
The forward initially checked in on loan in January 2023 and his move to Molineux was made permanent for £35m that summer.
Amid speculation about his future and a potential move away from Wolves, Cunha agreed a new four-and-a-half year contract, to run until 2029, in February. His original deal ran until 2027.
Last week, Wolves and Manchester United were at loggerheads as to how the £62.5m fee would be paid after the Red Devils signalled their intent to trigger Cunha's release clause.
United were keen to pay the hefty fee in five instalments over the Brazilian's five-year contract.
But Wolves were insistent the payment would be over three instalments across two years, as per the agreement in Cunha's contract. Wolves were determined that the influential attacker would not be allowed to leave on the cheap.
Cunha has agreed a five-year deal plus the option of another 12-months in Manchester.
The forward netted 17 goals in 36 appearances for Wolves across all competitions during the season.