He was born in Živinice, SR Bosnia and Herzegovina, but represented the clubs AK Sloboda Tuzla, AK Slavonija Osijek, AK Partizan and AK Crvena Zvezda in Belgrade. Before athletics, Dragan practised boxing. His former coaches were Nikola Tomasović, Dmitar Marceta and Veljko Čegar . His first European Championships was in 1990 in Split in his home country (then) Yugoslavia. Perić finished twelfth in the shot put final. He then finished seventh at the 1991 World Championships, seventh at the 1992 Olympic Games, fifth at the 1993 World Championships. In 1994 he won the silver medal at the European Indoor Championships, and finished sixth at both the 1994 European Championships and the IAAF Grand Prix Final. After that he won the bronze medal at the 1995 World Indoor Championships.