The Netherlands international has committed to a four-year contract with the option to extend for a further year.
Blind, who can play in midfield, at left-back and in central defence, said goodbye to his team-mates on Sunday before flying to England to complete a medical.
The 24-year-old was a key member of the Netherlands team who, under Louis van Gaal, finished third at the World Cup over the summer.
"It is a real honour to sign for Manchester United," Blind told the club's official website.
"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."
Blind becomes United's sixth signing this summer, while the club are also expected to complete a season-long loan for Monaco striker Radamel Falcao before the end of the transfer window.
"I am delighted Daley has signed for the club," said Van Gaal.
"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."