The 22-year-old, who will be in Manchester in the next 48 hours for a physical, will receive a guaranteed £80.75 million from United as well as an additional £4.25 million in add-on payments.
As talks between the two clubs proceeded, Antony was once again omitted off the Ajax roster for Sunday's game at Utrecht.
Transfer rumours for Man United
Premier League ins and outs during the 2022 summer transfer window
There should be no issues with personal terms in this agreement.
For several weeks, United has been after Anthony, and earlier this week, the club rejected a £67.9 million (€80 million) approach from United.
United has considered more options. They are interested in Pierre-Emerick Aubameyang, a striker for Barcelona, and they are still monitoring his condition. Aubameyang has been the subject of negotiations with Chelsea.
Cody Gakpo of PSV Eindhoven continues to be a target for United. It has been said that it is "unlikely but not impossible" to sign both Antony and Gakpo.
According to Antony, "Since February of this year, my agents came to Amsterdam to advise Ajax of my wish to leave the club and take on a new challenge and that other interested clubs would arrive and that there would undoubtedly be a big offer with them."
Meetings that included an Ajax proposal for contract renewal were concluded throughout the window months. I reiterated that I wish to quit the club.
"Today at a board meeting, I indicated interest in leaving the club and this time had a sizable offer on the table. Others have already arrived, but Ajax consistently objects on the grounds that it only has five days to replace them (me).
"I'm asking Ajax to sell me as the player who receives the best bid for an Eredivisie player; I'm not asking [for Ajax to release me]"
With Erik ten Hag, the ex-manager of Ajax, Antony would be reunited if he joined United. Ten Hag has already signed defender Lisandro Martinez from Ajax.
"I was really content in Amsterdam, where I won championships with Ajax, made friends, and developed a portion of my career. But today, I want to reiterate that I am prepared and motivated to pursue my tale and my aspirations," Antony said.
"People need to pay attention to me and realise that my driving force leads me to happiness. This is necessary for me to keep working hard. My affection for Ajax will never fade.
United has until Thursday at 11:59 p.m. (midnight) to finalise any additional transactions because the transfer window closes on Thursday.
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