Venegoor of Hesselink, 30, spent three years in Scotland after joining Celtic from PSV Eindhoven.
Related ArticlesTurner eyes England placeBrown defends Turner saleHull manager Phil Brown will be relieved to have boosted the club's attacking options after missing out on a number of targets this summer.
Michael Owen, Daryl Murphy and Bobby Zamora have all rejected the chance to move to the KC Stadium over recent weeks, leaving the Tigers' squad looking a little thin up front.
Brown did manage to recruit United States striker Jozy Altidore, however, on a season-long loan from Villarreal.
Hull chairman Paul Duffen claimed the club had beaten some big clubs to bring the striker to the KC Stadium.
"I'm delighted we have beaten off all the competition to bring him to the KC stadium.
"We've definitely wanted an experienced, top-drawer striker who scores goals and Jan has scored prolifically in top leagues in Europe.
"It's what we need. We didn't score enough goals last season. Going forward we have a lot of new talent and Jan will play his part in using his experience to settle them down.
"We've been looking at Jan since July and are really pleased we've turned his head.
"He's been looking at other big clubs in Europe but the Premier League is where he wants to come and play with us."