Leonidov was raised on an isolated farmstead in the province of Tver Oblast. The son of a farmer and woodsman, he went to work as a casual labourer at the docks in Petrograd. When an icon painter noticed Leonidov's drawing skills, he became his apprentice.
Career
In 1919 Leonidov attended the Svomas free art studios in Tver. From 1921 to 1927 he studied at the VKhUTEMAS in Moscow under the tutelage of Alexander Vesnin at which point his attention switched from painting to architecture.
His unexecuted diploma project in 1927 for the Lenin Institute and Library, Moscow, brought him international recognition. The scheme was prominently displayed at the Exhibition of Contemporary Architecture, Moscow, and was published in the OSA Group journal Sovremennaya arkhitektura. He then went on to teach at the VKhUTEMAS between 1928 and 1930.