Modi boarded the submarine and unveiled its plaque, after meeting veterans of the first Kalvari who were present at the ceremony.
"Kalvari is an excellent example of our 'Make in India' programme," he said, speaking at the commissioning ceremony here this morning.
Navy chief Admiral Sunil Lanba, National Security Adviser Ajit Doval and French Ambassador to India Alexandre Ziegler were among those present at the ceremony.
Modi thanked France for this 'strategic joint project' and described the commissioning of the submarine as a "matter of pride" for 125 crore Indians.
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Kalvari is named after the dreaded tiger shark, a deadly deep sea predator of the Indian Ocean.
"The power of Kalvari, that of a tiger shark, will strengthen our Navy," the prime minister said.
He said India has always been the first responder in times of crisis for neighbours, be it floods, water shortage or cyclones, in Sri Lanka, Maldives or Bangladesh.
During the Nepal earthquake, Indian Navy and Air Force rendered major assistance, he noted.
"So far this year, around 200 terrorists have been killed by police and security forces in Kashmir. There has been a reduction in the number of stone pelting incidents there," he said.
He said, "There has also been a decline in Naxal violence. This shows people are veering towards the path of development."
Defence Minister Nirmala Sitharaman said submarine building is a sophisticated and exacting craft which very few countries possess in their industrial capacity.
"India has proven its capability to build submarines for the past 25 years. These are highly significant steps in the direction of 'Make in India' and 'Skill India'. Making submarines benefits industry not only by itself through orders but also through stringent quality control," she said.
"Kalvari underwent around 120 days of extensive sea trials and tests for various equipment," a Navy official said, adding the vessel is expected to bolster India's maritime prowess.
The submarines, designed by French naval defence and energy company DCNS, are being built by Mazagon Dock Limited (MDL) in Mumbai as part of Project-75 of the Indian Navy.
"The technology utilised in the Scorpene has ensured superior stealth features such as advanced acoustic silencing techniques, low radiated noise levels, hydro-dynamically optimised shape and the ability to launch a crippling attack on the enemy using precision guided weapons," an official of the MDL said.
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