The 24-year-old Netherlands international, who can play as a defensive midfielder or on the left side of a back three, has put pen to paper on a four-year contract at Old Trafford after agreeing personal terms and passing a medical over the weekend after the clubs agreed the fee on Friday.
Blind, whose deal also includes the option of a further year, will link up once again with former Netherlands boss Louis van Gaal at Old Trafford.
He told United's official website: "It is a real honour to sign for Manchester United.
"I have been at Ajax since I was seven years old and I will always have very fond memories of the club and of my time there.
"Louis van Gaal is a tremendously talented coach, I have worked with him at Ajax and also for the Netherlands national team and I cannot wait to work with him at the biggest club in the world."
United manager Van Gaal said: "I am delighted Daley has signed for the club. He is a very intelligent and versatile footballer that can play in many positions.
"Daley is a great reader of the game, he has played under my philosophy over a number of years and he will be a great addition to the team."
Blind came through the youth ranks at hometown club Ajax and made his senior debut for the Amsterdam-based club in 2008.
He has made 19 appearances for the Netherlands and was voted Dutch Player of the Year for the 2013/14 season.