Ed Jaynes was born in Waterloo, Iowa, on 5 July 1922, the son of a surgeon. He attended Cornell College and the University of Iowa, receiving the B.A. degree in physics from the latter in 1942, and was then engaged in Doppler radar development at the Sperry Gyroscope Company in New York in 1942–43. He was subsequently appointed an Ensign in the U.S. Navy, and worked at the Naval Research Laboratory at Anacostia on microwave IFF equipment.

Lt(jg) Jaynes was discharged from the Navy in 1946 and spent that summer at Stanford working with W.W. Hansen on the design of the first linear electron accelerator. In the 1946–47 school year he was a graduate student at Berkeley, a student of J.R. Oppenheimer. When Oppenheimer left to take over the Institute for Advanced Study in Princeton in the summer of 1947, Jaynes also transferred to Princeton University. He received his Ph.D. in physics there in 1950, with a thesis in solid-state theory supervised by Eugene Wigner.

He then returned to Stanford, where he was Instructor, Assistant Professor, and Associate Professor during 1950–60. At this time he also consulted for Varian Associates on problems of magnetic resonance instrumentation. In 1960 he was appointed Professor of Physics at Washington University in St. Louis, and in 1975 became Wayman Crow professor of Physics.