Bračanin was born in Kalgoorlie, the son of Croatian immigrants. HIs early musical studies were with Miss Olive Ruane, and he graduated from the University of Western Australia in 1962 with bachelor's degrees in mathematics and music. He pursued graduate studies at the same school in musicology specialising in analysis of 20th-century music, earning an MA in 1968 and a PhD in 1970. His master's thesis was on the music of Mátyás Seiber and his doctorate thesis was on the music of Anton Webern. From 1970 to 2008 he served on the staff of the University of Queensland. For 9 years he was Dean of the Faculty of Music and 10 years Head of the School of Music and is now Emeritus Professor. Professor Bracanin served on the boards of the Australian Music Centre, Queensland Philharmonic Orchestra, Queensland Symphony Orchestra and 4MBS Classic Radio.
Bračanin initially began composing music in the 1970s for the purposes of creating music that would more effectively teach his students certain aspects of harmony and counterpoint. He eventually became interested in creating more serious compositions for their own sake, with his 1977 Trombone Concerto being now regarded as his first mature work. He has since produced a considerable body of music, including symphonic works, choral works, chamber music, and pieces for solo piano. Many works by Bračanin are published by the Australian Music Centre and Maecenas Music. He has occasionally been musically inspired by the Dalmatian Croatian musical heritage of his forebears. In 1988 Bračanin was composer in residence at the Anglo-Australian Music Festival in Birmingham, England. In 1991, he fulfilled a similar role at the Bournemouth International Festival, at which two of his works were performed, including a festival commission. In 1995 his Guitar Concerto won the APRA Award for the best Australian Classical Composition.