Antony becomes the second-most expensive signing in United’s history after the £89.6m arrival of Paul Pogba from Juventus in 2016.
Newsonline report that United are set to pay a guaranteed €95m (£81.3m) to Ajax, with an additional €5m (£4.2m) in add-ons.
The Brazil international is reunited with his former Ajax manager Erik ten Hag, who he had played under since joining from Sao Paolo in 2020.
“This is an incredible moment in my career to be joining one of the most iconic clubs in the world,” Antony said.
“I’m thankful to everyone who has believed in me, especially my family, and all my coaches and teammates, 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 and coaching brings out the best in me, and I am excited by what he has told me about his plans and ambitions in Manchester.
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“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, and I can’t wait to join my new team-mates and play my part in bringing success to Manchester United.”
John Murtough, United’s football director, said: “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.