Both clubs confirmed the move on their official websites on Monday morning.
The 21-year-old Portugal youth international has played only once for the Toffees' first team - in last season's Capital One Cup third-round defeat at Leeds - since arriving in January 2012 from Benfica.
Vitesse finished fourth in the Eredivisie last term but failed to reach the Europa League group stage, losing to Romanian side Petrolul Ploiesti in the two-legged qualification round.
The player will join Christian Atsu in the Arnhem squad, the Ghana winger having on Sunday become the fifth Chelsea player to be loaned to the Dutch club, following Lucas Piazon, Patrick van Aanholt, Cristian Cuevas and Gael Kakuta.
- Sports & Recreation
- Petrolul Ploiesti
- Christian Atsu