Sources told ESPN FC the fee for the 28-year-old is £14.1 million, possibly rising to £18.5m with add-ons, giving United a slight profit on the £13.8m they paid Ajax for his services in 2014.
A statement issued by United on Monday read: "We have agreed terms with Ajax for the transfer of Daley Blind. A further announcement will be made in due course."
The deal has been expected for some time, and the Netherlands international was not part of the United squad that flew to Los Angeles for their preseason tour on Sunday night.
Blind met up with the Ajax squad at their training base at St George's Park on Monday, sources said. The Dutch side are due to play in England next week against Wolves and Walsall.
At United, Blind was a regular under former boss Louis van Gaal but struggled to establish himself Jose Mourinho and was restricted to just four Premier League starts last season.
In four years at Old Trafford, Blind made 141 appearances in all competitions, scoring six times.
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