Ajax have confirmed Blind has been withdrawn from the Dutch champions' squad for Sunday's trip to Groningen after United agreed a fee of £13.85million for the 24-year-old.
A statement from Manchester United read: "Manchester United is delighted to announce it has reached agreement with Ajax to sign Daley Blind, subject to a medical and personal terms.
"A further announcement will be made when the process is complete."
Manager Louis van Gaal is keen to strengthen his squad after a disappointing start to the Premier League season, losing at home to Swansea on the opening day before drawing at Sunderland last weekend.
And, with summer signing Luke Shaw injured, van Gaal wants the versatile Blind to provide serious competition for several places in the team.
After the 0-0 draw with Burnley, he said: "He'll come to Manchester to have a medical, and then we might have a new player."
United are currently undergoing a significant overhaul of their squad, having completed a British transfer record £59.7million deal to sign Angel di Maria from Real Madrid.
The likes of Danny Welbeck and Tom Cleverley have been told they are no longer wanted by the club while several other players are set to depart.
The 20-time English champions have been linked with a move for Arturo Vidal, but are understood to be cautious about bidding for the Juventus midfielder due to his knee injury.
Another reported target is Roma's Kevin Strootman, but he again is also just coming back from injury.