Krebs, the son of an ear, nose, and throat specialist, was born in Hildesheim, Germany, was educated at the universities of Göttingen, Freiburg, Munich, Berlin, and Hamburg, obtaining his MD in 1925. He taught at the Kaiser Wilhelm Institute, Berlin, and the University of Freiburg but in 1933, with the growth of the Nazi movement, decided to leave Germany. Consequently he moved to England, where from 1935 to 1954 he served as professor of biochemistry at Sheffield University; after 1945 he was appointed director of the Medical Research Council's Cell Metabolism Unit at Sheffield. In 1954 Krebs moved to Oxford to take the Whitley Chair of Biochemistry, a post he held until his retirement in 1967.

Krebs is best known for his discovery of the Krebs cycle (or tricarboxylic acid cycle) in 1937. This is a continuation of the work of Carl and Gerty Cori, who had shown how carbohydrates, such as glycogen, are broken down in the body to lactic acid; Krebs completed the process by working out how the lactic acid is metabolized to carbon dioxide and water. When he began this work little was known apart from the fact that the process involved the consumption of oxygen, which could be increased, according to Albert Szent-Györgyi, by the four-carbon compounds succinic acid, fumaric acid, malic acid, and oxaloacetic acid. Krebs himself showed in 1937 that the six-carbon citric acid is also involved in the cycle.

By studying the process in pigeon breast muscle Krebs was able to piece together the clues already collected into a coherent scheme. The three-carbon lactic acid is first broken down to a two-carbon molecule unfamiliar to Krebs; it was in fact later identified by Fritz Lipmann as coenzyme A. This then combines with the four-carbon oxaloacetic acid to form the six-carbon citric acid. The citric acid then undergoes a cycle of reactions to be converted to oxaloacetic acid once more. During this cycle two molecules of carbon dioxide are given up and hydrogen atoms are released; the hydrogen is then oxidized in the electron transport chain with the production of energy. Much of the detail of this aspect of the cycle was later filled in by Lipmann, with whom Krebs shared the 1953 Nobel Prize for physiology or medicine.

Krebs fully appreciated the significance of the cycle, pointing out the important fact that it is the common terminal pathway for the chemical breakdown of all foodstuffs.

In 1932, with K. Henselheit, Krebs was responsible for the introduction of another cycle. This was the urea cycle, whereby amino acids (the constituents of proteins) eliminate their nitrogen in the form of urea, which is excreted in urine. This left the remainder of the amino acid to give up its potential energy and participate in a variety of metabolic pathways.