The two clubs have agreed a £13.8 million fee, while the 24-year-old is now set to hold contract talks with United.
A statement from Ajax read: "Ajax and Manchester United have reached an agreement over the transfer of Daley Blind for a fee of €17.5 million [£13.8m]. His contract with Ajax was due to expire in June 2016. The agreement is subject to the fulfilment of a number of conditions."
Louis van Gaal is keen to strengthen his defensive options following the arrival of Marcos Rojo from Sporting, although the Argentina international has not yet obtained a work permit and is still unavailable for selection.
Blind, who told Goal earlier in August that he would find it difficult to turn down a move to Old Trafford, primarily plays as a left-back but is capable of covering in central defence and midfield.
Blind is set to become United's sixth signing of the summer following the arrivals of Ander Herrera, Luke Shaw, Vanja Milinkovic, Rojo and Di Maria, who joined from Real Madrid in a deal worth £59.7m on Tuesday.