Hofmann was born in Munich in 1903 and the son of the German chemist Karl Andreas Hofmann. He studied chemistry at the Technical University of Berlin and obtained a diploma in 1925. He went on to receive his doctorate in 1926 from his father with the work Glanzkohlenstoff und die Reihe des schwarzen kristallinen Kohlenstoffs (Lustrous carbon and the series of black crystalline carbon). In 1931 he received habilitation on graphite oxide and then worked as a lecturer at the Technical University of Berlin.
In 1937, Hofmann became a member of the NSDAP. In the same year, he also became a professor of chemistry and the head of the Institute of Chemistry at the University of Rostock. He did only a short military service in World War II, since he was released for war-related work. In 1942 he became head of the Institute for Inorganic and Analytical Chemistry at the Technical University of Vienna, where he also installed an electron microscope by Manfred von Ardenne. In 1945, Hofmann left Vienna and from 1948 taught chemistry and set up his laboratory at the Philosophical-Theological University of Regensburg (now University of Regensburg), where no chemistry had previously been taught. In 1951, he became professor of inorganic and physical chemistry at Technical University of Darmstadt. In 1960, Hofmann became head of the Institute for Inorganic Chemistry at the University of Heidelberg, where he later retired in 1971.