Over the course of his career that spanned almost three decades, Stojanović, a goalkeeper,[1] played for Crvena zvezda (two spells), Zagreb, Partizan, Mepamsa San Antonio, Conquense, THW Kiel, VfL Bad Schwartau, HSV Hamburg, and SC DHfK Leipzig.

[2] He won numerous trophies at club level, including the EHF Cup with THW Kiel in the 1997–98 season.

He was also a member of the team that finished runners-up at the 1990 Goodwill Games, winning the silver medal.

Later on, Stojanović competed for FR Yugoslavia, winning the bronze medal at the 1996 European Championship.

In April 2013, Stojanović was appointed as head coach of AMTV Hamburg for the 2013–14 season.