Hoff spent his adolescence in Budapest, where he went to the same high school that had been attended by Leo Szilard, Eugene Wigner, and John von Neumann. After high school, he enrolled at Eidgenössische Technische Hochschule Zurich, where he studied under Aurel Stodola. He graduated with an engineering degree in 1928.
In 1938, Hoff moved to America, in order to study solid mechanics under Stephen Timoshenko, receiving his Doctor of Philosophy from Stanford University in 1942. His plans to return to Hungary were interrupted by the onset of the Second World War. In 1940, Hoff joined the Polytechnic Institute of Brooklyn as an instructor in aeronautical engineering, eventually becoming full professor in 1946 and head of the Department of Mechanical and Aerospace Engineering in 1950.
He subsequently joined the faculty of Stanford University in the fall of 1957.
He served as the chair of the American Society of Mechanical Engineers Applied Mechanics Division (1955).
