Goran Bregović was born in Sarajevo to a Croat father and a Serb mother. His father was an officer in the Yugoslav People's Army. His parents divorced and he remained living with his mother in Sarajevo. Goran played violin in a music school, however, deemed untalented, he was thrown out during second grade. His musical education was thus reduced to what his friend taught him until Goran's mother bought him his first guitar in his early teens. Upon entering high school, Goran joined the school band Izohipse where he began on bass guitar. Soon, however, he was kicked out of that school, too (this time for misbehaviour). Bregović then entered grammar school and its school band Beštije (again as a bass guitar player). When he was sixteen, his mother left him and moved to the coast, meaning that other than having a few relatives to rely on, he mostly had to take care of himself. He did that by playing folk music in a bar in Konjic, working on construction sites, and selling newspapers.

Spotting him at a Beštije gig in 1969, Željko Bebek invited 18-year-old Bregović to play bass guitar in his band Kodeksi, which Goran gladly accepted.

Eventually, Kodeksi shifted setup so Goran moved from bass to lead guitar, resulting in Kodeksi having the following line-up during summer 1970: Goran Bregović, Željko Bebek, Zoran Redžić and Milić Vukašinović. All of them would eventually become members of Bijelo dugme at some point in the future. At the time, they were largely influenced by Led Zeppelin and Black Sabbath.

In the autumn of 1971 Goran entered university and decided to study philosophy and sociology. He soon quit, however. In the same time Milić Vukašinović left for London, so Goran and Zoran started playing in a band, named Jutro (trans. "Morning"). The band in the next few years transformed a lot and on January 1, 1974 the band changed its name to Bijelo dugme ("White Button"). Rock group Bijelo dugme (White Button) were one of the most popular bands of SFR Yugoslavia right from their arrival on the scene during mid 1970s until their folding in late 1980s.

At the time Bijelo dugme was falling apart, Goran entered the world of film music. His first project was Emir Kusturica's Time of the Gypsies (1989) which turned out a great success (both the film and the music from it). Goran and Emir's collaboration continued, and Goran composed music (which was performed by Iggy Pop) for Emir's next film Arizona Dream (1993). His next major project, music for Patrice Chéreau's Queen Margot was again a great success, and the film won two awards on the 1994 Cannes Film Festival. Next year's Golden Palm went to Underground, for which Goran Bregović composed the music.

Bregović's music carries both South Slavic and Romani themes and is a fusion of popular music with traditional polyphonic music from the Balkans, tango and brass bands.

Since 1998 he is performing his music mainly in the form of concerts all over the world with his Weddings and Funerals Orchestra, which consists of 10 people (in the small version) or 37 (in the large version, although at some instances this number will be different, depending on participants from the host country). The small orchestra consists of Alen Adamovic (vocals, drums), Bokan Stankovic (first trumpet), Dalibor Lukic (second trumpet), Stojan Dimov (sax, clarinet), Aleksandar Rajkovic (first trombone, glockenspiel), Milos Mihajlovic (second trombone), Dejan Manigodic (tuba) and Goran himself. The uniqueness of the orchestra comes from the voices of the Bulgarian singers Daniela Radkova-Aleksandrova and Ludmila Radkova-Traikova. The large orchestra usually has singers from the Belgrade Orthodox male choir, string performers from Poland or from the country where they perform, as well as other local performers.