He started his pro club career with Aix Maurienne Savoie, of the French 2nd Division, in the 1993–94 season.
In 2003, he moved to Montepaschi Siena, where he won the first Italian League championship in the club's history.
During his pro career, Vukčević played in the European-wide top-tier level EuroLeague, in a total of 10 seasons,[4][5] and he made it to the league's Final Four three times, in 1999, 2003, and 2004.
Vukčević began working as a basketball coach in 2022, when he joined the Greek Basket League club Peristeri Athens.
Their older son, Tristan (born 2003), is a professional basketball player that has played in the NBA with the Washington Wizards.