Born into a family of film-makers (his father was a cinematographer and his mother was film editor), Milicevic started playing piano when he was 6. He received a B.A. in music composition (1982) and an M.A. (1986) in music composition and multimedia arts from the Music Academy of Sarajevo, in his native Bosnia and Herzegovina, where he studied with Josip Magdic. Milicevic came to the United States in 1986 to study with Alvin Lucier at Wesleyan University in Connecticut, where he received his master's degree in experimental music composition (1988). After Wesleyan, he went to study with Dennis Kam at the University of Miami in Florida, where he received his doctorate degree in computer and experimental music composition in 1991.
In the nineties, Milicevic has concentrated on live interactive electronic music composition utilizing hyper instruments. He was awarded several music prizes for his compositions in the former Yugoslavia as well as in Europe. Milicevic worked in Yugoslavia as a freelance composer for 10 years, where he composed for theater, films, radio and television, also receiving several prizes for this body of work. Since he moved to the United States in 1986, Milicevic has performed his live electronic music, composed for modern dances, made several experimental animated films and videos, set up installations and video sculptures, had exhibitions of his paintings, and scored for films. His film music can be heard at his website http://myweb.lmu.edu/mmilicevic/ba/
He presents on variety of topics at many international conferences ranging from film, music, religion, psychology and neuroscience of (film, music, and religion,) sociology, aesthetics, cultural studies, and education. Milicevic is very interested in interdisciplinary connections among all these disciplines. For example, in education, he is using brain based learning in order to improve his teaching effectiveness. Milicevic's most popular class at Loyola Marymount University is Movie Music class, where he approaches film music from the neuroscientific and psychological point of view.
In former Yugoslavia, Milicevic (under alias name Igor Krik) produced the 1985 pop band, VALENTINO, that sold platinum.
In 2003, he composed the score for the cult film The Room, directed by Tommy Wiseau. He later wrote the score for Wiseau's 2004 documentary Homeless in America, and in 2015 it was announced that he will also be scoring the documentary about The Room, titled Room Full of Spoons.
In 2009, he also produced an album entitled "I’ve got a song for you" by Rade Šerbedžija and Miroslav Tadić. For this work, he was nominated for the PORIN award in Croatia as the best-produced album.
He scored a documentary, Cuba: The Forgotten Revolution, which won an Emmy in 2016.