The Dutch club have confirmed on their official website that Zuiverloon is heading to the Premier League side.
Reports in Holland suggest the fee for the 21-year-old, who was under contract at Heerenveen until 2010, is around £3.2million.
The youngster has been a regular in the Heerenveen side for the past two seasons after starting his career at Feyenoord.
He has been included in Holland's squad for the Olympic Games in Beijing in August and was part of the team which won the European Under-21 Championship last summer.