Komogorov was born on 28 July 1927 in Moscow, then part of the Russian Soviet Federative Socialist Republic, in the Soviet Union. He lived throughout the Axis invasion and occupation of parts of the Soviet Union during the Second World War, during which time he worked as an apprentice fitter at the Moscow Tool Plant from the age of fourteen. He completed secondary school in 1949 and entered Moscow State University of Economics. Graduating in 1954, he went to work for the Ministry of Forestry and Woodworking Industry, and in roles in the State Planning Committee and the .