In March 1958, a few months after the launch of Sputnik 1, a competition was announced for the best design of an obelisk celebrating the dawn of the Space Age. Out of some 350 proposals, the design by sculptor A.P. Faidysh-Krandievsky and architects A.N. Kolchin and M.O. Barshch was chosen. The grand opening of the monument took place on October 4, 1964, on the day of the 7th anniversary of the Sputnik 1 launch.

The monument was designed to accommodate a museum in its base. However, it took until April 10, 1981 (two days before the 20th anniversary of Yuri Gagarin's flight) to complete the preparatory work and open the Memorial Museum of Cosmonautics. The museum reopened on April 12, 2009, after three years of renovations.