The 20-year-old, who represented the Netherlands at the Under-21 European Championships, will undergo a medical with the Eredivisie champions before penning a four-year deal.
"It's great that everything has come around so fast," Van der Hoorn told Voetbal International. "I will be on the training ground for the first time on Wednesday, before the medical, and presentation.
"With Ajax I get a great new challenge."
Van der Hoorn's arrival increases speculation about the future of highly-rated Belgian centre-back Toby Alderweireld.