Zec was born in the town of Rogatica to a Bosniak family, he graduated from the School of Applied Arts in Sarajevo in 1964. In 1969 Safet Zec graduated from the University of Fine Arts in Belgrade, and then in 1972 completed his postgraduate studies at the same university.
In the seventies, Safet Zec became one of the major exhibits of poetic realism. He was one of the most famous artist in Yugoslavia during the early nineties. Until 1989, he lived and worked in Belgrade with his family, he returned to Sarajevo the next year. He left the country in 1992 because of the Bosnian War, and fled to Udine, Italy.
Safet Zec has prepared over 70 solo exhibitions in Bosnia and Herzegovina and in large cities around the world. He is also a member of the Association of Visual Artists of Bosnia and Herzegovina. He has won over 20 awards and is acknowledged for his work. In 2007 he was awarded with the Order of the Arts and Literature of France. His works are in major European and international galleries, as well as private collections.