He started his career at Borac Banja Luka. Still young, he moved to FK Partizan youth team. Where he played until 2000. While in Serbia, he also played for FK Teleoptik and FK Milicionar Beograd. Vuković became a citizen of Poland on 13 June 2008. He has signed a contract with new club – Iraklis Thessaloniki F.C. on 17 December 2008.