The Netherlands international featured in 21 games in all competitions for Stoke, starting eight Premier League matches.
His departure comes as Mark Hughes' side completed a stunning £18.3m deal for Porto star Giannelli Imbula.
Van Ginkel has so far played just a handful of games for his parent club Chelsea, who are eager for him to get more experience in the Eredivisie.
He moved to Stamford Bridge from Vitesse Arnhem in 2013 and also spent last season on loan with AC Milan.