Vennegoor of Hesselink once hit 22 goals in a season for PSV Eindhoven, scoring 76 goals in all from 157 appearances for the club.
He signed a three-year deal with Celtic in August 2006 for a fee of around £3.4m, and scored 38 goals for the Scottish side.
Vennegoor of Hesselink made his international debut in October 2000, and has scored five times for his county in 27 appearances. But he has yet to feature in the Netherlands' World Cup 2010 qualifiers.
Meanwhile, goalkeeper Boaz Myhill has signed a new three-year deal at the KC Stadium.
The 26-year-old Wales international, who joined from Aston Villa six years ago, is now committed until 2012.
Myhill, who has played for the Tigers in all four professional divisions, has re-established himself as the club's first-choice goalkeeper after losing his place to Matt Duke for a spell midway through last season.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.