Antony is set to join Manchester United after the Premier League club agreed a £81.3million (€95m) fee with Ajax.
Ajax reportedly turned down a bid of £76.4m (€90m) for the winger last week, one of several offers United made to the Eredivisie champions.
A deal, which Ajax on Tuesday revealed could rise to £85.6m (€100m) with add-ons, has now been reached between the clubs for the 22-year-old, who was again left out of Ajax's squad to face Utrecht on Sunday.
The transfer is set to go through ahead of Thursday's transfer deadline, subject to a medical, personal terms being finalised and international clearance.
Antony's omission from the Ajax squad last weekend came after he publicly pleaded with Ajax to sell him to United in an interview with journalist Fabrizio Romano.
In the interview, Antony explained he informed Ajax of his intention to leave the club as early as February.
Antony will become United's fifth signing under Erik ten Hag, whose side have won their past two Premier League games after losing their opening two matches.
Lisandro Martinez will present Antony with a familiar face in the squad, having also joined from Ajax – Ten Hag's former club – while Tyrell Malacia arrived from Feyenoord.
Former Ajax, Tottenham and Inter playmaker Christian Eriksen arrived on a free transfer after leaving Brentford, and United last week signed Casemiro from Real Madrid.
Antony scored 12 goals for Ajax in all competitions last season, and is capable of playing across the forward line.
With doubts remaining over Cristiano Ronaldo's future at Old Trafford, he will seemingly come in as competition for Marcus Rashford, Anthony Martial and Jadon Sancho, while it has been suggested Anthony Elanga may be allowed to leave United on loan.