The Netherlands midfielder has completed a medical with United ahead of a £40m deal, expected to be completed after the international break.
"This is a dream come true," Andre van de Beek told Omroep Gelderland. "Our local village is very proud.
"It's the perfect moment for him to make this step to such a beautiful club, but Ajax will always remain in our heart.
"A lot of clubs were interested, but Donny took this decision himself."