The edifice of four storeys had three wings opening toward the Senate, which a central building which faced Taynitskaya Garden to the south connected.

The southern facade had an Ionic colonnade and a gabled roof in the center, reflecting the Neoclassical style of the adjacent Senate Building.

The Presidium was on the site of the former Chudov Monastery which Metropolitan Alexius of Moscow founded in 1365, Ascension Convent, and Lesser Nicholas Palace.

These were among the historic edifices in the Kremlin that Joseph Stalin ordered demolished as part of the state atheism campaign, pursuant to which religious structures throughout Russia were razed.

In 2014 President Vladimir Putin proposed the restoration of the former Chudov Monastery, Ascension Convent, and Lesser Nicholas Palace.