Cardinal Bozanic was born on 20 March 1949 in Rijeka (Yugoslavia - now Croatia). His was a farming family, but his brother Antun is also a priest and he is related to a Bishop Bozanic from the 19th Century.
He has a Masters in Dogmatic Theology from the Pontifical Gregorian University and a Masters in Canon Law from the Pontifical Lateran University.
He was ordained a priest on 29 June 1975 and had various pastoral and curial roles in the diocese of Krk, including as the Bishop's secretary and teaching at the local seminary.
Pope John Paul II appointed him Coadjutor Bishop of Krk on 10 May 1989. He was consecrated on 25 June 1989 in Krk by Cardinal Franjo Kuharic, Archbishop of Zagreb. He succeeded to full governance of the diocese of Krk on 14 November 1989. He was appointed administrator of the Archdiocese of Rijeka-Senj on 5 June 1996 and was later appointed Archbishop of Zagreb on 5 July 1997.
He is President of the Croatian Conference of Bishops and Vice-President of the Council of European Bishops' Conferences.
Pope John Paul II elevated him to the College of Cardinals on 21 October 2003, giving him the title of San Girolamo dei Croati.