The warship, which is expected to sail into Indian waters in December, was commissioned by Western Naval Commander Vice- Admiral Shekhar Sinha, the Navy said in a release.
The first warship of the series, INS Teg, had joined the naval fleet earlier this year.
Armed with the 290-km range supersonic BrahMos cruise missile, the warship is part of the follow-on Talwar class project.
It is also equipped with upgraded 100 mm medium range gun, optically controlled 30 mm close-in weapon system, torpedoes, rocket launchers and advanced electronic warfare suite.
"The induction of stealth frigate with an advanced combat suite and blend of Russian and Indian cutting edge technologies, will bolster our role as a key facilitator in promoting peace and stability in Indian Ocean region," the Navy said.
"The warship is commanded by Captain Antony George -- an anti-submarine warfare specialist, and will join the Western Fleet by December end," it said.
Ambassador of India to Russia, Ajai Malhotra attended the induction ceremony along with senior officials of the Russian government and the United Shipbuilding Corporation.
The Russian Navy has also placed orders for three warships with a similar configuration for its own requirements with the Yantar shipyard.
