The 18-year-old was signed by Chelsea from NK Zadar earlier this month but is being sent to the Dutch league to gain experience, following on from Cristian Cuevas and Lucas Piazon, who both went to Vitesse Arnhem earlier this month.
NAC said on their website (www.nac.nl) that Perica had signed for the season. He is a lanky under-21 international, who the club said would add a new dimension to their attack.
Chilean midfielder Cuveas was also recently bought by Chelsea but Brazilian prospect Piazon has already played for the London club and spent the last six months on loan at Malaga.
Vitesse will also have Chelsea duo Patrick van Aanholt and Gael Kakuta for a second season on loan.