The 25-year-old will join United on a deal running until June 2030, with the option to extend for a further year.
Cunha impressed last season with 17 goals and six assists in all competitions for Wolves, attracting attention from top clubs across Europe.
His performances at Molineux followed previous spells at Atlético Madrid and RB Leipzig. The transfer fee will be paid in instalments over two years, after United's initial proposal to spread payments over four or five years was rejected.
Although the club has announced the transfer, Cunha's move is still subject to visa approval and registration. Once completed, he will become United's latest addition as they look to bolster their attacking options ahead of the new campaign.
Internationally, Cunha has earned 15 caps for Brazil, scoring his first senior goal in March against Argentina. Known for his pace, technical ability and versatility across the front line, he is expected to bring dynamism and depth to Erik ten Hag's squad.
"It is hard to put into words my feelings about becoming a Manchester United player," Cunha said in a statement released on Thursday.
"Ever since I was a child in Brazil watching Premier League games on TV at my grandmother's house, United was my favourite English team and I dreamed of wearing the red shirt. I want to thank my family and everyone who has helped me make that dream a reality.
"I can't wait for the start of preseason to get to know my teammates and prepare for the season ahead. All my focus is now on working hard to become a valuable part of the team, and helping get this club back to the top."
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