The Krasnodar, launched in 1985, was decommissioned in 2012, RIA Novosti reported.
It will be the last submarine to be dismantled at the Nerpa shipyards in Murmansk.
The Russian Navy has decommissioned 199 nuclear submarines since the late 1980s, with 50 scrapped at Nerpa since 1998. Russia has three shipyards capable of dismantling nuclear submarines.
Removal of the spent nuclear fuel is a first step in scrapping nuclear submarines. The bow and stern will be cut away and destroyed, while the reactor compartment will be sealed and put into storage.
Destruction of the Krasnodar is expected to be completed by 2014, Nerpa officials said.