He was born in Nilsby, Sweden. He emigrated to the USA in 1907 and entered the University of North Dakota in 1912. He received a Ph.D. in physics at Yale University in 1917. He worked at AT&T from 1917 to 1934, then moved to Bell Telephone Laboratories.
As an engineer at Bell Laboratories, he did important work on thermal noise ("Johnson-Nyquist noise") and the stability of feedback amplifiers.
His early theoretical work on determining the bandwidth requirements for transmitting information, as published in "Certain factors affecting telegraph speed" (Bell System Technical Journal, 3, 324-346, 1924), laid the foundations for later advances by Claude Shannon, which led to the development of information theory.
In 1927 Nyquist determined that an analog signal should be sampled at twice the frequency of its highest-frequency component in order to be converted into an adequate representation of the signal in digital form. Nyquist published his results in the paper Certain topics in Telegraph Transmission Theory (1928). This rule is now known as the Nyquist-Shannon sampling theorem.
He retired from Bell Labs in 1954.
Nyquist died in Harlingen, Texas.
See: Nyquist plot.