Antony will undergo a medical at Manchester United within the next 48 hours.
Ajax has agreed to sell the Brazilian winger for an initial fee of £80.75m, with a further £4.25m in add-ons.
The Brazilian would become Manchester United's joint-second most expensive signing alongside defender Harry Maguire.
Antony scored 25 goals and provided 22 assists in 82 appearances for Ajax, who he joined from Sao Paolo in 2020.
The attacker would become United's fifth signing of the summer, joining Lisandro Martinez, Casemiro, Tyrell Malacia and Christian Eriksen.
