Garayev was born on November 13, 1956 in Baku, Azerbaijan. He graduated from the Azerbaijan University of Languages in 1978. From 1978 until 1980, he worked as the teacher of English in a secondary school in Saatly Rayon. In 1980-1989, he held various positions within the Azerbaijan Communist Party. In 1992, he completed a course at the North-West Academy of Public Administration in Russia. In 1992 through 1993, Garayev worked as a professor at the Azerbaijani Academy of Public Administration. In 1993-1994, he held several managerial positions at Improtex Commerce.
From 1994 to 2001, Garayev was Minister of Youth and Sports of Azerbaijan. He was briefly appointed as Minister of Youth, Sports and Tourism in a cabinet reshuffle in 2001 and later was appointed as Minister of Culture and Tourism in 2006.