The striker is currently with the France national team at Clairefontaine, but has today been allowed to leave to join United from Monaco.
A statement on the French Football Federation website read: "He (Martial) requested from Didier Deschamps permission to travel to England to sign a contract with Manchester United.
"Given the exceptional circumstances, the coach has accepted to the request of the player."
Anthony Martial edges closer to Manchester United move
Martial's arrival looks to coincide with the departure of Javier Hernandez, who was pictured by German newspaper Bild arriving at Bayer Leverkusen ahead of a permanent move.
The uncapped Martial, who has been likened to Arsenal legend Thierry Henry, was called up by Deschamps for friendlies against Portugal and Serbia.
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