Giorgadze was born in Zaisan, a city on the Soviet-Chinese border in what is now Eastern Kazakhstan. His father General Panteleimon Giorgadze, a World War II veteran and the former head of United Communist Party of Georgia, wanted his son to receive military education. In 1968 Giorgadze got accepted at the prestigious Higher School of the USSR Committee for State Security (KGB) in Moscow. He graduated in 1973 with a degree in Jurisprudence and foreign languages. Besides Georgian and Russian, he speaks Turkish and French as well as Serbo-Croatian and Azeri.