A native of Rijeka, he started playing basketball in his home town clubs before joining the Nikola Vujčić Academy.
After playing for Split, Zagreb and Zabok in August 2016 he joined another A-1 Liga team: Vrijednosnice Osijek.
[2] After averaging 10 points and 7.5 rebounds per game during the 2019-20 season, Vuković had his contract with Zadar extended for two years on May 20, 2020.
[3] In April, 2022, Vuković fell to an injury of his achilles tendon which kept him off the court for more than six months.
[4] In February, 2024, Vuković left the financially-troubled Cibona for a more lucrative contract with the Taiwanese Tainan TSG GhostHawks playing in the T1 League.