The 18-year-old Burkina Faso international joined Chelsea in 2013, but was not able to officially put pen-to-paper until January 1 this year, and within 24 hours he had joined Vitesse.
He played more than a dozen games for Vitesse and will return to the Gelredome for next season.
Technical manager Mo Alllach told the Vitesse website: 'We are delighted Bertrand will join us again. He knows our way of working and our kind of style, also he impressed us with his personality."
The Traore deal is just the latest deal between Vitesse and Chelsea, who have an ongoing relationship over players, with Brazilian defender Wallace also heading to the club for next season.
Patrick van Aanholt, Lucas Piazon and Christian Atsu all spent last season on loan at Vitesse, but they will not be heading back.
The two clubs have also announced that they will be playing a friendly in Holland on July 30.