The 22-year-old has signed a five-year contract at Old Trafford with the option for a further year and becomes Manchester United's fifth summer signing after Tyrell Malacia, Lisandro Martinez, Christian Eriksen and Casemiro.
Antony joined Ajax from Sao Paulo in the 2020 winter transfer window and won two Eredivisie titles, both under Manchester United manager Erik Ten Hag.
"This is an incredible moment in my career to be joining one of the most iconic clubs in the world," Antony told United's official website.
"I'm thankful to everyone who has believed in me, especially my family, and all my coaches and team-mates, because I could not have got here without them.
"Playing under Erik ten Hag at Ajax was perfect for me and my development. His style of football brings out the best in me, and I am excited by what he has told me about his plans and ambitions in Manchester.
"My time at Ajax was fantastic and I will always be grateful for the trust they put in me, but now I am ready for the next challenge.
"I can't wait to join my new team-mates and play my part in bringing success to Manchester United."
Manchester United football director John Murtough added: "Antony is one of the most exciting young talents in European football and has exactly the right profile for the attacking, dynamic team Erik is building.
"We have been especially impressed by his desire to join Manchester United, and to be part of a long-term project to get the club back to the levels of performance we all expect."
