He has appeared in several successful Danish films from the 1990s and 2000s, frequently appearing in films directed by Nicolas Winding Refn, including Bleeder and The Pusher Trilogy: Pusher, Pusher II & Pusher III. For his role in Pusher, he won the Bodil Award for best supporting actor in 1997.
In 1981 he moved to Denmark. He married Sonja Hindkjaer, with whom he has three children. After divorce, he married Dragana Milutinović, on 7 October 1998.
In 2009, Burić had a large supporting role in the apocalyptic film 2012, as Yuri Karpov, a Russian Billionaire. In 2012, he repeated his role as Milo in the British remake of Pusher.
