He started studying Philosophy and Theology in Rijeka and transferred to Zagreb, where he graduated from the Catholic Faculty of Theology in 1975. Bozanić was ordained as a priest of the Diocese of Krk on June 29, 1975 in Krk. His first service was of an episcopal secretary of the Bishop of Krk, Karmel Zazinović.
In the period between 1976 and 1978 he served as a chaplain in Mali Lošinj and rector of the parish Ćunski and after that a rector of the parish Veli Lošinj. In 1978 he was once again appointed the episcopal secretary of the Bishop of Krk.At the same time he enrolled in a postgraduate study at the Catholic Faculty of Theology in Zagreb and in the fall of 1979 he earned an academic degree of a Master of Theology in Dogmatic Theology.
The bishop of Krk sent him to Rome, where as a student of the Pontifical Croatian College of St.Jerome he continued his study of Theology at the Pontifical Gregorian University and study of canon law at the Pontifical Lateran University thus earning an academic degree of a licentiate in canon law.
Upon his return from Rome he was appointed Chancellor of the Bishop's Ordinary in Krk (1986-1987) and Vicar General of the Diocese of Krk (1987- 1989) . In the period between 1988 and 1997 he taught Dogmatic Theology and Canon Law at the Catholic Faculty of Theology in Rijeka.
Holy Father John Paul II appointed him Bishop Coadjutor of Krk on May 10, 1989. He was ordained bishop on June 25, 1989 in the Krk Cathedral. His Consecrator was the Archbishop of Zagreb Cardinal Franjo Kuharić and co-consecrators were Msgr. Josip Pavlišić, the Archbishop of Rijeka and Senj, and Msgr. Karmelo Zaninović, the Bishop of Krk. On November 14, 1989 he was appointed diocesan bishop of Krk.
At the Bishop's Conference of Yugoslavia and later at the Croatian Bishops’ Conference he served as the president of the Council for laity, vice president of the newly established Commission Justitia et Pax and president of the Committee for the Great Jubilee. He was a member and president of the Bishops’ Commission for the Pontifical Croatian College of St. Jerome in Rome.
Since the Croatian Bishop's Conference was constituted in 1993, he was a member of the Permanent Council of the CBC in all terms.In 1993 he was elected member and then a president of the Commission of the Croatian Bishops’ Conference for state relations.
In that period agreements between the Holy See and the Republic of Croatia were prepared and signed.
Pope John Paul II appointed him the Archbishop of Zagreb on July 5, 1997. Bozanić took over his service of Archbishop of Zagreb and Metropolitan on October 4 of the same year in the Zagreb Cathedral from his predecessor Cardinal Franjo Kuharić.
He was elected president of the Croatian Bishops’ Conference that year as well, office he held for two consecutive terms till 2007. As the Archbishop of Zagreb he is the Great Chancellor of the Catholic Faculty of Theology of the University of Zagreb and Great Chancellor of the Catholic University of Croatia.
At the 36th plenary session of the Croatian Bishops’ Conference in 2008 he was elected president of the CBC's Commission for relations with the European Union and at the 41st plenary session of the CBC in 2010 the vice president of the CBC and president of the episcopal commission of the CBC for state relations.
In April 2001 he was elected first vice president of the Council of European Bishops' Conferences (CCEE) and in 2006 he was re-elected to the same duty for another term. He participated in the first ( in 1991) and the second (in 1999) Special Assembly for Europe of the Synod of Bishops. At the second one, he was elected member of the Special Council of the General Secretariat for Europe of the Synod of Bishops in Rome on the topic: The Word of God in Life and Mission of the Church.
He is a member of the Congregation for Divine Worship and Discipline of Sacraments, Congregation for Catholic Education, Pontifical Council for the Laity and newly established Pontifical Council for Promoting New Evangelization as well as a member of several special commissions of the Holy See.
In 1998, as the Archbishop of Zagreb and president of the CBC, he greeted Pope John Paul II in Zagreb during his second official papal visit to Croatia and in Marija Bistrica at the ceremony of beatification he asked him to beatify Cardinal Alojzije (Aloysius) Stepinac. In 2003, once more as the president of the CBC, he greeted Pope John Paul II during his third official papal visit to Croatia when he visited Rijeka and Trsat, Dubrovnik,Osijek, Đakovo and Zadar.
On October 21, 2003 Pope John Paul II elevated him to the College of Cardinals of the Roman Catholic Church at the ceremonious Consistory in Rome.
He participated in many international symposiums in Croatia and abroad and published several scientific articles in Croatian and international publications. In 2008 his books: Istina u ljubavi i Blaženi Alojzije Stepinac – baština koja obvezuje [Truth in love and the Blessed Aloysious Stepinac – a binding heritage – tr.] were published, and in 2009 one more was published: Čovjek, Crkva i domovina u otajstvu Uskrsa i Božića [Man, Church and Homeland in Mystery of Easter and Christmas - tr].
His latest book: Krist vas zove. Poruke mladima [Christ is calling you. Messages to youth] was published in 2011 and is dedicated to youth who have shown their enthusiasm in their meeting during the official papal visit of Pope Benedict XVI to Croatia.
Pope Benedict XVI appointed him member of the Pontifical Council for Social Communications on December 29, 2011.