Noether was born into a Jewish family in Karlsruhe, Grand Duchy of Baden, German Empire in 1915.
The following four years, during World War II, he served with US Army intelligence in England, France, and Germany.
He worked in academia for the rest of his career, beginning at New York University.
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.
The initial recipients of the Gottfried E. Noether Senior Scholar Awards were Erich Leo Lehmann (2000), Robert V. Hogg (2001), and Pranab K. Sen (2002).