The Brazil youth international will link up with three of his fellow Blues in a loan move that will see the 19-year-old play for the Dutch side until the end of the season.
The 19-year-old was brought to the club as a youth player two years ago from Brazilian side Sao Paulo and made his debut last season before going on to make a further two appearances in all competitions.
He gained his first taste of regular first-team football on loan to Spanish side Malaga during the second half of last season and will now continue his development with a move to the Eredivisie.
Piazon will join a strong contingent of Chelsea youngsters at the club and, linking up with fellow teammates Patrick van Aanholt, Cristián Cuevas and Gael Kakuta.
The Brazil winger will be hoping to add to the 13 appearances he made during his stint in Spain last season, which included two appearances in the Champions League as Malaga reached the quarterfinals.
Piazon is Vitesse's the sixth new signing under new manager Peter Bosz, with the Eredivisie side having opened its league campaign with a 3-1 home victory over Heracles Almelo last Sunday.