From 2010 to 2013, Vukčević played for local club Budućnost, where he earned 65 caps and scored four goals.

Vukčević left Budućnost as a free agent due to the expiration of his contract.

He made his debut for the club in a 3–0 win against Vitória S.C., coming on as a 91st-minute substitute for Felipe Pardo in the Minho derby.

On 9 August 2018, Vukčević moved to Spanish club Levante for a €8.9 million fee and signed a four-year contract.

[4][5] In August 2012 he participated in the Valeri Lobanovsky Memorial Tournament 2012, where his team lost in the final to Slovakia on penalties and took home silver medals.