The 21-year-old has been loaned out for the fifth time in his career and is the third Chelsea player to join the Dutch club this summer after Wallace and Bertrand Traore.
McEachran last featured for Chelsea in January 2012 and has since had loan spells at Swansea City, Middlesbrough, Watford and Wigan Athletic.
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The 21-year-old has been hailed as the brightest English talent to emerge from the Blues' academy in a decade but has failed to establish himself in the first-team squad at Stamford Bridge.
McEachran, an England Under-21 international, is the third Chelsea player to be loaned to Vitesse this summer after Brazilian defender Wallace and Bertrand Traore.
"Josh is a talented player who can play as a controlling midfielder," said the Dutch club's technical director Mo Allach. "I have seen Josh several times last season so his qualities are well-known to us and we are convinced that he can show them here."