Cunha, 26, has been a key player for Wolves, scoring 33 goals in 92 appearances over two-and-a-half seasons. He has also represented Brazil 13 times at the senior level.
Before joining United, Cunha will play for Brazil in their World Cup qualifier against Ecuador on Friday night.
United has confirmed the signing in a statement, saying they look forward to welcoming Cunha to Old Trafford.