The numbers five and three in the Eredivisie booked their places in freezing temperatures on Wednesday night with wins of 3-0 against Willem II and 4-0 against FC Twente respectively.
AZ made the final last year but lost 2-0 to Vitesse. They last picked up the trophy in 2013. Feyenoord have played in 17 finals and won the cup 12 times, the last of which was against FC Utrecht in 2016.
The final will take place in the Kuip stadium in Rotterdam on April 22.