Rakić was born in Sarajevo on 11 April 1931, in Bosnia and Herzegovina.
After graduating, he became an Assistant Professor for physiology and biochemistry at the University of Belgrade's School of Medicine.
Rakić was the founder of the International brain research laboratory in Kotor where lots of famous scientists worked.
Between 1960 and 1980, he was a Visiting Professor of the University of California and, during the 80's, at the Baylor College of Medicine in Houston.
Rakić's chief area of scientific research was in CNS and cancer and genetic therapy of tumors.