The 19-year-old was linked with Tottenham earlier this summer before penning a new contract at Stade Louis II but now becomes Louis van Gaal’s sixth summer signing for a reported fee of £36 million (€50m).
Martial, who was handed his first senior call-up to the France squad this week, was given permission to leave the international camp and complete a move Monaco claim could eventually be worth £58.7m (€80m).
“I’m so excited to join United,” said Martial upon signing a four-year contract with the option for a further year. “I’ve always wanted to play in the Premier League and I look forward to meeting my team-mates.”
Manager Van Gaal added: “Anthony is a talented young forward with great potential. I believe this is the club for him to continue his development.”
With Robin van Persie joining Fenerbahce in July and Javier Hernandez expected to leave for Bayer Leverkusen, signing a new striker has been United’s top priority before the close of the transfer window.
Wayne Rooney is currently enduring his worst run of form in the Premier League since moving to Old Trafford in 2004, having not scored 10 games as he adapts back from last season’s deeper role.
Martial has been identified as one of the hottest properties in French football and it has been reported in France that Monaco boss Leonardo Jardim threatened to quit were he sold to United.
The youngster arrives at Old Trafford with only 52 senior appearances to his name, but his eventual transfer fee could come in just shy of Angel Di Maria’s British record £59.7m move to United in August 2014.