It will ply the seas alongside the former Russian aircraft carrier "Admiral Gorshkov", now the "INS Vikramaditya", due to be delivered by year-end after a delay of more than four years.
India has been Russia's top arms customer for years, but relations have frayed over delays and cost-overruns.
India is spending tens of billions of dollars upgrading its mainly Soviet-era military hardware. India unveiled the 6,000-ton INS Arihant -- Destroyer of Enemies -- in 2009 as part of a project to built five such vessels which would be armed with nuclear-tipped missiles and torpedoes.
Prime Minister Manmohan Singh said he was "delighted to learn that the nuclear propulsion reactor on board INS Arihant, India's first indigenous nuclear powered submarine, has now achieved criticality".
Criticality refers to the point at which a nuclear reaction is self-sustaining.
Singh described the development as "a giant stride in the progress of our indigenous technological capabilities" and said he hop