Despotopoulos was born in Smyrni, Asia Minor (today's Izmir, Turkey) in 1903; soon after he was born, his family moved to the island of Chios where he grew up. He moved to Athens to study architecture. He was enrolled student at the National Technical University of Athens (N.T.U.A.) until he quit and left to study at the Bauhaus in Weimar. He then moved to Leibniz University Hannover, graduating from there in 1927.
It was 1930 when he returned to Greece By 1943 (during the occupation of Greece by Nazi Germany), Ioannis Despotopoulos became Professor at the School of Architecture at the N.T.U.A. In 1946, he was discharged from his position at the university and he moved to Sweden for a period between the years 1947 and 1961. During his stay in Sweden, he worked as an architect and also taught at the Polytechnic Institutes of Stockholm and Goeteborg. He returned to Greece in 1961 and appointed immediately as a professor at the N.T.U.A. until 1968 when he retired. He died in 1992