The 24-year-old is likely to serve as a replacement for wantaway centre-back Niklas Moisander, according to Sky Sports News.
"We wanted to have him and we're happy that it worked out," said Ajax director of football Marc Overmars.
"Nick is at a good age and has played over 200 matches of professional football. He's playable centrally on defence and also as a left back and at midfield.
"All in all, a reliable player who can be used in several positions at Ajax."
Viergever, who has earned one cap for the Dutch national team, joined AZ Alkmaar in 2010 after progressing through Sparta Rotterdam's academy.