The Moroccan World Cup hero has completed a deadline day loan move as Erik ten Hag finally secures a new defensive midfielder.
Amrabat, 27, has been chased by the Red Devils for much of the summer, and was keen on the move, turning down interest from other sides.
Now complicated negotiations have finally been completed, with Amrabat becoming Ten Hag's seventh signing of the window.
United have forked out almost £7million for the loan fee, with the club having a £17m buy option plus £4.3m in add-ons.
Speaking of his delight at the move, the Morocco international told the club's website: "It is a huge honour to become a Manchester United player.
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"I've had to be patient for this moment. But I'm someone who always listens to my heart and now I am representing the club of my dreams.
"I am a passionate player; I want to bring that energy to the squad, and I will put everything into every action I take for the team.
"I know exactly how Erik ten Hag likes to work and what he needs from his players.
"His coaching and guidance developed me so much as a player earlier in my career.
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"I know that he will help to bring out the best of my abilities so that I can help the group to be successful this season."
United's director of football John Murtough added: "We have tracked Sofyan for a long time, so we are really pleased to bring him to Manchester United.
"His committed, high-energy approach to the game fits perfectly with the group that we are building here.
"We know that Sofyan's mentality, dynamism and technical qualities will help the squad as we look to achieve success in all competitions this season."