 Topsøe was born on 24 May 1913 in Copenhagen, Denmark, as son of captain Flemming Topsøe (1885–1954) and Hedvig Sofie Topsøe (1888–1961).After graduating from Frederiksberg Gymnasium in 1931, he started studying physics under Niels Bohr and chemistry at the Technical University of Denmark.He became a master of Science in Engineering in chemistry in 1936.