Taube, who was born in Saskatchewan, Canada, moved to America in 1937 and became naturalized in 1942. He was educated at the University of Saskatchewan and the Berkeley campus of the University of California, where he gained his PhD in 1940. After working at Cornell University (1941–46), Taube moved to Chicago and in 1952 was appointed professor of chemistry, a post he held until 1962 when he accepted a comparable appointment at Stanford, California.

As a leading inorganic chemist Taube has succeeded in developing a range of experimental techniques for studying the kinetics and mechanism of inorganic reactions, in particular electron-transfer reactions. Transition metals such as iron, copper, cobalt and molybdenum form coordination compounds of a type first described by Alfred Werner. In a typical coordination compound a metal ion is attached to a number of ligands, such as water or ammonia. It was thought that the ligands would keep the ions apart and inhibit electron transfer between ions. Taube showed experimentally that ligand bridges form between interacting complexes, thus allowing electrons to be transferred.

For his work in this field Taube was awarded the 1983 Nobel Prize for chemistry.