The terms to bring the 20-year-old to Ajax were agreed between the clubs last Saturday, but it has taken until now for the deal to be completed.
"I am very happy with this contract and am looking forward to starting training soon," Van der Hoorn told the club's official website.
"I have signed a contract for four seasons. Ajax have been champions for the last three years so I hope that will continue.
The player has been capped four times by the Dutch Under-21s.