The 20-year-old will move to Stamford Bridge subject to a medical, and the agreement of personal terms.
The midfielder scored eight league goals last season as the Arnhem club finished fourth in the Eredivisie, their highest position for 15 years, and he was also voted the Dutch young player of the year.
He made his senior debut with the Netherlands national team against Germany in November last year, coming on as a late substitute in their 0-0 friendly in Amsterdam.
A statement on Chelsea's website read: "Chelsea Football Club and Vitesse Arnhem have reached an agreement for the transfer of Marco van Ginkel.
"The player will join Chelsea subject to a medical, agreement of personal terms and legal documentation."
He would become Jose Mourinho's second summer signing following the arrival of Andre Schurrle from Bayer Leverkusen.