Originally from Bundoora, Victoria,[1] Veszpremi was drafted by Sydney from the Northern Knights in the TAC Cup with the eleventh selection in the 2007 AFL Draft. He was named in the Under 18 All Australian side as a defender, but also played as a forward, where he once kicked eight goals for the Knights in a final.[2]
Veszpremi made his debut for Sydney in round 18, 2008 against the Western Bulldogs in a 16-point defeat. In his fourth game, against Brisbane, Veszpremi kicked four goals.[1]
Veszpremi was one of five teenage footballers whose final year of junior football was chronicled in the book The Draft: inside the AFL's Search for talent by Emma Quayle, published by Allen and Unwin in September 2008.[3]
At the end of the 2010 AFL season, Veszpremi was traded to the Western Bulldogs.[4] He, along with a late draft pick, were traded for Bulldogs player, Andrejs Everitt.[4]