Noether emigrated to the United States in 1939, where he earned a bachelor's degree (1940) and a master's degree (1941). The following four years, during World War II, he served with US Army intelligence in England, France, and Germany. After the war, he earned a doctorate from Columbia University (1949).
He worked in academia for the rest of his career, beginning at New York University. He moved to Boston University in 1952 where he worked until he joined the faculty of the University of Connecticut in 1968. There, he eventually became chairman of the department of statistics. He retired in 1985.
Noether served on a statistical advisory committee for the United States Office of Management and Budget and as an associate editor of The American Statistician. He was a fellow of the American Statistical Association and the Institute of Mathematical Statistics.
In 1999 the Gottfried E. Noether Awards were established to "recognize distinguished researchers and teachers and to support research in the field of nonparametric statistics."