The Netherlands Under-21 international, who was set out as a summer target for the London club, is expected to complete his move in the next few days
The 20-year-old's move to Stamford Bridge is subject to a medical and the agreement of personal terms, with the fee believed to be in the region of €10.5 million.
Goal exclusively revealed in May that Chelsea were set to secure the services of the youngster, who has been tipped to become a leading star for the Netherlands and shone during the Under-21 European Championships.
The midfielder was recently named Netherlands 'Talent of the Year' after his stellar season with Vitesse, scoring eight goals and helping them to secure Europa League football for the upcoming season.
His performances last season also earned a first senior call-up to Louis van Gaal's national squad for a friendly against Germany in which he made his debut coming on as a substitute.
Chelsea's close relationship with the Dutch outfit has helped secure the services of Van Ginkel, having previously sent the likes of Gael Kakuta and Patrick van Aanholt on loan to help the club's growth.