Born in Ochamchira, Abkhaz ASSR, Georgian SSR, Gvazava graduated Sukhumi Pedagogical Institute with a degree in biology in 1974 and continued his postgraduate training at the Institute of Medical Genetics in Moscow from 1976 to 1981.
In May 1978, several thousands of Abkhaz nationalists assembled in the village of Lykhny to support 130 Abkhaz Communists, who had signed the letter to Moscow, demanding that the Abkhaz ASSR be allowed to be transferred from Georgia to the Russian SFSR.