Nouhak was born at Ban Phalouka in Mukdahan Province in 1910, according to official sources, although his year of birth has also been given as 1914. He married for the first time in 1933 and re-married in 1944. He was a founding member of the Lao revolutionary movement in 1945, and he became Chairman of the Lao Resistance Committee for the Eastern Region in 1949. In the Lao Resistance Government, he was named Minister of Finance in 1950. He participated in the founding congress of the Lao People's Party (later renamed the Lao People's Revolutionary Party, LPRP) in 1955 and was elected as a member of its Central Committee.
Nouhak was subsequently the Secretary of the Lao People's Party cell in Vientiane, the capital, and was a member of the National Assembly in 1958. He was arrested in 1959 and spent a year in prison in Vientiane before escaping along with Souphanouvong. He was then Secretary of the party cell in Khangkhay and had important roles in the party during the 1960s and 1970s, while the Laotian Civil War was ongoing. He was elected to the Politburo at the LPRP's Second Congress in February 1972 and was assigned responsibility for economic affairs.
When the Pathet Lao took power in December 1975, Nouhak was appointed as Deputy Prime Minister and Minister of Finance. For years, he was considered "Number 2" in the leadership under Prime Minister Kaysone Phomvihane. He was elected as First Vice-Chairman of the Council of Ministers in April 1982, then as a standing member of the Council of Ministers in charge of economic affairs in November 1986. Nouhak was subsequently elected to the Supreme People's Assembly in 1989 and became President of the Supreme People's Assembly in the same year; also in 1989, he was chosen as chairman of the commission charged with drafting a new constitution, which was adopted in 1991. With the adoption of this constitution, Kaysone assumed the presidency, which was transformed from a ceremonial to an executive position. After Kaysone's death, Nouhak was elected to succeed him as President of Laos by the Supreme People's Assembly in an extraordinary session on November 25, 1992.
Despite the presidency's executive powers, Prime Minister Khamtai Siphandon held the country's most powerful position as General Secretary of the LPRP. When Khamtai decided to move from Prime Minister to President in 1998, Nouhak Phoumsavanh—who was by then one of the oldest heads of state in the world—retired, leaving office on February 24, 1998.
Nouhak remained on the Central Committee and Politburo of the LPRP until the party's Sixth Congress in 1996. At the Sixth Congress in 1996 and the Seventh Congress in 2001, he was named as adviser to the Central Committee's Executive Committee. He reportedly remained in good health throughout his old age, and he was said to have continued making visits to the provinces by helicopter until 2007. He died on September 9, 2008. The state news agency attributed his death simply to "old age", while noting that he had received medical treatment both in Laos and outside the country. A committee of 26 members, including leading party and state figures (with President Choummaly Sayasone as its chairman), was formed to organize his funeral, and a five day national mourning period was declared for September 10–14, during which time all entertainment was prohibited. He was cremated in Vientiane on September 14.