Born in Lansing, Iowa, Krebs was educated at the University of Illinois and Washington University, Seattle, gaining his MD in 1943. For the following two years he worked as an intern and assistant resident at Barnes Hospital, St. Louis, and in 1946 returned to Washington University as a National Institutes of Health research fellow. In 1968, by now professor of biochemistry, Krebs moved to a similar position at the University of California, Davis. In 1977 he again returned to Seattle as professor of pharmacology in the school of medicine. In the same year he joined the Howard Hughes Medical Institute as investigator, becoming senior investigator in 1980 and emeritus professor in 1991.

Krebs is perhaps best known for his work on the regulation of enzyme activity, which he did at Seattle in conjunction with the biochemist, Edmond Fischer. For this, he and Fischer shared the 1992 Nobel Prize for physiology or medicine.