Yusif Veliev was born on March 22, 1917 in Derbent. From 1933 to 1936 he was educated at the Baku Theatrical College. In his student years, he played in the massive performances of the Drama Theater. After 1949 he studied at the Theatrical Technicum in the Shekinsk State Dramatic Theater. The debut role of Yusif Veliev was the episodic role of one of the commissioners in the film Bakhtiyar (1955). Veliev was played in more than 30 film, in the film studio "Azerbaijanfilm".
In the 1960, Yusif Veliyev was the honored artist of Azerbaijan, and in 1979 he was the People's Artist of Azerbaijan. The actor died on 18 March 1980.