The ceremony for the laying of the Museum's foundation stone took place on August 17, 1898 in the presence of Tsar Nicholas II and members of his family. The name of the museum – Alexander III Fine Arts Museum – was officially approved. Building work had commenced a month before that ceremony, which was important as by then the Committee for the Establishment of the Museum already had at its disposal a major part of its collections.

The Museum was created on the basis of Moscow University's "Cabinet of Fine Arts and Antiquities" which had been set up as both a public museum and one for educational purposes. In it the main stages in the history of art from ancient times until the post-Renaissance era were represented through casts, models, painted copies and galvanocopies. This museum was the first of its kind in Russia. Work to create it had been initiated (1893) by the highly respected Professor Ivan Tsvetaev (1847-1943), who had a doctorate in Latin literature and art history and was later to be the Museum's first director (1911-1913).

At the end of 1896 a competition to design the building for the Museum was announced and 19 architects from various cities in Russia took part. From among the entrants the University Board selected Moscow architect, Roman Klein (1858-1924), to build the Museum. It was constructed in keeping with the latest building techniques and principles of museum practice. The design was based on the model of a Classical temple on a high podium with an Ionic colonnade along its façade. The interior decoration combined elements drawn from the various historical periods represented by the exhibits. Engineers I.I.Rerberg and V.G.Shukhov were involved in the construction work.