Burzan attended school in Titograd, then part of Yugoslavia.
He became a professor at the University of Montenegro in the Department of Natural Sciences pursuing research in physics; he there from 1976 through 1998, although he became active in politics by the late 1980s.
In 1992, he was one of the founders of the Social Democratic Party of Montenegro (SDP) and was elected to Parliament, where he served from 1992 through 1996.
During his time in Parliament, he participated in and initiated numerous conferences, seminars, initiatives and networks aimed to end the various wars going on in the Balkans at the time.
He also organized and supported civil society initiatives in Montenegro and the Balkans in general, with an emphasis on human rights, including co-founding the weekly Monitor newsletter.