Nam had been battling testicular cancer for the past few years and his condition had worsened with age, his family added.
Nam, who earned a doctorate in economics at Oklahoma State University, was appointed finance minister by President Park Chung-hee in 1969 and served in the role until 1974. From 1974 to 1978, Nam was deputy prime minister in charge of economic policies during South Korea's industrial development.
Before entering public service, Nam had been an economics professor at Sogang University in Seoul. Park is said to have recruited Nam after reading the scholar's criticism of the government's economic policies.
Under President Chun Doo-hwan, Nam was the prime minister from 1980 to 1982. Then from 1983 to 1991, Nam served as the head of the Korea International Trade Association.
After leaving the government, Nam continued to lend his expertise to politicians. Before the presidential election in 2007, Nam worked alongside current President Park Geun-hye, daughter of Park Chung-hee who was then vying for the ruling party's candidacy, as a senior economic adviser.
Nam is survived by his wife and three children.