Krebs was born in 1900 to a Jewish family in Hildesheim, Germany, where his father was a doctor. After studying medicine successively at the universities of Göttingen, Freiburg and Munich he served, amongst other positions, as Research Assistant to the pioneering biologist Otto Warburg in the Kaiser Wilhelm Institut für Biologie, Berlin-Dahlem, from 1926 to 1930, and then at the Municipal Hospital of Altona. In 1931 he moved to the Department of Medicine at the University of Freiburg, gaining international recognition for the discovery of the ornithine cycle when his work was published the following year. But the accession to power of the Nazis early in 1933 led quickly to his dismissal and flight to England, where it had proved possible to offer him a relatively minor post in Cambridge. In 1935 he moved to Sheffield, having obtained a lectureship, initially in pharmacology but three years later transferring to biochemistry, and where his second major discovery, of the citric or tricarboxylic acid cycle was made and published in 1937 (remarkably, the journal Nature turned down this paper when it was offered to them and it was published in Enzymologia). During the war years he worked on nationally important research relating to diet and nutrition, particularly the role of vitamins, as a member of Sheffield's Sorby Institute. In 1945 the Medical Research Council set up a Unit for Research in Cell Metabolism at Sheffield, as head of which Krebs was given Professorial status, and which remained in being under his leadership until his retirement in 1967, though transferring with Krebs and most of his research team to Oxford in 1954. The Sheffield period saw the award to Krebs of two major honours: Fellowship of the Royal Society in 1947, and the Nobel Prize for Physiology and Medicine (jointly with Franz Lipmann) in 1953. Many other honours and awards followed during the rest of his career.

In 1954 he was offered and accepted the Whitley Chair of Biochemistry at Oxford University, and his MRC work continued in the Metabolic Research Laboratory in the Radcliffe Infirmary. In 1958 he received a knighthood. Although officially retiring in 1967 he continued to work, funded by the MRC and other grants, until his death in 1981 at the age of 80.

There is as yet no complete full-scale biography. Krebs published a memoir 'Reminiscences and reflections', in collaboration with Anne Martin, Clarendon Press 1981, and there is a two-volume biography up to the year 1937 by Frederic Lawrence Holmes, 'Hans Krebs', Oxford University Press, 1991-93.