Traore signed for Chelsea in January before immediately making a temporary move to Eredivisie club Vitesse.
The 18-year-old scored three goals in 15 league appearances in that spell as Vitesse finished sixth in the Dutch top flight.
And the Arnhem club have now agreed to retain the Burkina Faso international's services for another campaign.
"We are delighted that Bertrand has joined us again," Vitesse technical director Mo Allach told the club's official website.
"He is familiar with our work and playing style and his personality has impressed us."
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