Born in Zloczow, Poland (now Zolochez in Ukraine), Hoffmann was moved at the age of four with his family to a labor camp. His father was executed for trying to escape, but Hoffmann and his mother were smuggled out in 1943 and spent the rest of World War II hiding in the attic of a schoolhouse. Hoffmann has noted that only 80 of the 12,000 Jews of Zloczow survived the war. Following the liberation in mid-1944, Hoffmann's mother returned to Poland and emigrated with her son to America in 1949; he became a naturalized citizen in 1955.

Hoffmann was educated at Columbia and at Harvard, where he obtained his PhD in 1962. He moved to Cornell in 1965 and was appointed professor of chemistry in 1974.

In the mid-1960s Hoffmann began a research collaboration with R. B. Woodward on molecular orbital theory. Their work led to the formulation in 1965 of what are now known as the Woodward-Hoffmann rules. These laid down general conditions under which certain organic reactions can occur. The rules apply to pericyclic reactions. In reactions of this kind bond breaking and formation occur simultaneously without the presence of intermediates, i.e., they are said to be ‘concerted’ reactions. The reactions also involve cyclic structures. Woodward and Hoffmann published their work in their Conservation of Orbital Symmetry (1969). Hoffmann's collaboration with Woodward won him a share of the 1981 Nobel Prize for chemistry with K. Fukui; Woodward's death in 1979, however, robbed him of his second Nobel Prize.

Hoffmann has also published two volumes of verse, The Metamict State, and Gaps and Verges. He has also written and presented a number of television programmes, The World of Chemistry and The Molecular World, in which he has attempted to introduce chemistry to a wider audience. A similar approach can be seen in his The Same and Not the Same (1995), in which he tries to describe for a popular audience how the world behaves at the molecular level.