Born in the north-western Bosnian town of Bihać (then Socialist Federal Republic of Yugoslavia), Kožul was awarded the title of Grandmaster by FIDE in 1989.

Also in 1990, Kozul won the bronze medal playing for the Yugoslav team at the Chess Olympiad in Novi Sad.

[1] After the break-up of Yugoslavia, Kozul played for Bosnia and Herzegovina, and he was a part of the Bosnian team in the Olympiad 1992.

In 1993, Kozul, an ethnic Croat, settled in Croatia, thereafter representing that country.

[7] In April 2017, he finished tied for first with Nikita Vitiugov, Etienne Bacrot and Maxim Matlakov in the Grenke Chess Open in Karlsruhe, Germany.