On 2 April 2019, Vuković was appointed manager of Legia Warsaw, having previously worked there in assistant and caretaker roles. In the 2019–20 season, he led the team to their 14th Ekstraklasa title.[1] He was dismissed in the following season, after quickly dropping out of a UEFA Champions League qualifying and a league defeat at Górnik Zabrze.[2]
On 13 December 2021, he was once again announced as the manager of Legia, following Marek Gołębiewski's resignation a day prior after a defeat to Wisła Płock, which saw Legia drop to the bottom of the league.[3] In his first match after his return, Legia defeated Zagłębie Lubin 4–0 and left the relegation zone.[4] He successfully led Legia away from relegation and finished 10th, eleven points clear of the relegation zone, winning 3–0 against Cracovia on the last match day.[5] On the same day, Vuković left his role as Legia's manager.[6]
On 27 October 2022, he replaced Waldemar Fornalik as the manager of Piast Gliwice.[7] On 14 May 2024, shortly before the conclusion of the 2023–24 season, Piast announced they had exercised an option in Vuković's contract to keep him at the club until June 2025.[8]
Personal life
He was granted Polish citizenship on 13 June 2008.[9]