The Potters announced that the Dutch international has signed a four-year contract with the club, after they agreed a fee of just over £3m with the Eredivisie side.
Stoke's chief executive Tony Scholes told the club's website: "Erik has a considerable amount of experience of playing at the highest level, both on the international stage with Holland and in the Champions League with PSV Eindhoven.
"He is a player who was identified by our technical director Mark Cartwright as one who could strengthen our defensive options and we have been tracking his progress, so we are delighted to have brought him here now."
Manager Mark Hughes added: "I am delighted to have secured Erik's signature. The main focus this summer in attempting to strengthen the squad is ensuring it is balanced in key positions. We need good quality in our starting eleven and good quality back-up for all areas, which Erik will certainly give us defensively."
The 24-year-old has 17 caps with the Netherlands.