He was born into a large family on September 15, 1945, in Selnica, the parish of Marija Bistrica, to Janko and Agata née Salar. After completing primary school, he enrolled in the seminary gymnasium in the Šalata section of Zagreb. At the end of his second year at the gymnasium, he joined the Society of Jesus. Upon graduating from the gymnasium, he studied philosophy and theology at the Institute of Philosophy and Theology of the Society of Jesus in Zagreb.
On June 24, 1973, he was ordained to the priesthood. Following his ordination, he continued his studies at the Pontifical Gregorian University in Rome, where he earned a baccalaureate in moral theology in 1975 and a doctorate in 1984.
From 1977 to 1979, he was a member of the editorial board of the Croatian program broadcast by Vatican Radio.
After completing his studies, he returned to Zagreb and became a professor of moral theology at the Institute of Philosophy and Theology of the Society of Jesus. From 1990 to 1994, he taught Bioethics at the Pontifical Gregorian University in Rome. He was also a professor of Christian Ethics at the Faculty of Philosophy of the Society of Jesus in Zagreb.
He particularly distinguished himself in the field of bioethics and founded the Center for Bioethics at the Institute of Philosophy and Theology of the Society of Jesus in Zagreb. He was also engaged in research at the Joseph and Rose Kennedy Institute of Ethics u Washington, D.C., the Linacre Centre for Healthcare Ethics in London and the Institut Borja de Bioètica u Barcelona.
From 1990 to 1993, he was a member of the Council of the Croatian Conference of Bishops for the Doctrine of the Faith. In 1991 he became the ecclesiastical assistant of the Croatian Catholic Medical Society and in 1996 the ecclesiastical assistant of the European Federation of Catholic Medical Associations.
From 1994 to 2000, he was the rector of the Faculty of the Society of Jesus on Jordanovac. He published many scientific articles in scholarly journals and was the author of a number of books on moral theology.
On February 2, 2005, Pope John Paul II appointed him Titular Bishop of Petina and Auxiliary Bishop of the Archdiocese of Zagreb. His episcopal ordination took place on the Feast of St. Joseph, March 19, 2005, in the Cathedral of the Assumption of Mary in Zagreb.
On May 13, 2017, Pope Francis accepted Msgr. Pozaić’s resignation from the office of Auxiliary Bishop of the Archdiocese of Zagreb due to health reasons.
The funeral for the late Bishop Pozaić of blessed memory will be conducted by the President of the Croatian Conference of Bishops, Archbishop Dražen Kutleša of Zagreb, on Friday, May 19, at 12:30 p.m. at the Mirogoj Cemetery in Zagreb. Following the funeral, at 2:30 p.m. a Requiem Mass will be offered for the repose of his soul by Archbishop Emeritus Cardinal Josip Bozanić in the Blessed Alojzije Stepinac Place of Worship in Zagreb.