United confirmed a deal was in place earlier this week understood to be worth a fixed fee of £80.6million with a further £4.2m in add-ons.
The 22-year-old will be reunited with former Ajax boss Ten Hag, who has already raided his old club for defender Lisandro Martinez.
‘This is an incredible moment in my career to be joining one of the most iconic clubs in the world,’ said Antony upon confirmation of his signing.
‘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 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.
‘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, Manchester United Football Director, who played a key part in brokering the deal, 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.’
Ten Hag is hopeful that Antony will make his debut for the club against Arsenal on Sunday.
United face Leicester at the King Power Stadium on Thursday night and Antony would have to be registered before midday on Wednesday in order to play, which has been ruled out.
That means Antony will first be available to play for his new club against league leaders Arsenal, who visit Old Trafford on Sunday.
Asked if Antony could play against the Gunners, Ten Hag said in a press conference today: ‘I hope so.’