Aach was born in Oldenburg. He gained his doctorate in March 1952 in the Faculty of Mathematics and Natural Sciences of the University of Göttingen. In July 1961 he presented his professorial thesis at the University of Cologne. On 31 December 1962 he was appointed Extraordinary Professor of Botany at the RWTH Aachen University. From 12 January 1965 he was appointed to the Chair of Botany in the same place and made director of the Botanical Institute. He retired on 1 March 1984.
The emphasis of his scientific work was on proteins in viruses. He collaborated on the Handbuch der Biologie.