Babayev was born in
Baku,
Azerbaijan. In 1980, he graduated from the International Economic Relations department at
Taras Shevchenko National University of Kyiv in
Ukraine. He started his career working as an inspector at the Chamber of Commerce of Azerbaijan Republic. In 1981, he was assigned to work as foreign exchange inspector and later assistant manager of economy department at the USSR Foreign Economic Relations Bank. After the collapse of
Soviet Union, he was employed as the representative of
Xariciiqtisadibank in
Turkey. In 1997, he was elected Vice President of
Mostbank and was assigned to lead its chapter in
Great Britain. ==Political career==