Blind, 24, joins United on a day when they are also set to complete the loan signing of Monaco striker Radamel Falcao.
Ajax have confirmed the transfer on their official website.
Reports in Holland suggest the agreed fee is 18 million euros (£14.2 million), with United then also confirming the deal on the club's official Twitter account, although they said the fee was slightly lower at £14m.
"It's an honour to sign for United. I can't wait to work with Louis van Gaal at the biggest club in the world," Blind said.
He has signed a four-year contract at the club with the option of a further year.
Blind was part of Louis van Gaal's World Cup squad and is the son of former Netherlands defender Danny Blind.
The Ajax youth academy product can play in a variety of positions, including left-back and in central midfield.
Blind becomes the club's fifth summer signing.
Louis van Gaal and Daley Blind (PA Sport)
"I am enormously proud to be at one of the biggest clubs in the world," the 24-year-old Blind told Fox Sports television as his transfer was sealed before the transfer window ends on Monday.
He can play left back and as a defensive midfielder but said it did not matter in which position United used him.
"I don't mind at all, as long as I get minutes on the field," he said.
Van Gaal added: "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 should become the commanding holding midfielder that United so badly need and, with Falcao due to arrive, suddenly Man Ut'd squad is looking pretty handy. Still, they have spent almost £150m, so it's no big surprise. They are still short at centre-back and could do with another midfielder, but Blind plugs a few holes thanks to his versatility.
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- Louis van Gaal
- Danny Blind
- Radamel Falcao