Defence Minister Nirmala Sitharaman, Navy chief Admiral Sunil Lanba and top defence officials were present at the commissioning ceremony here.
On the occasion, Modi said Kalvari is an excellent example of 'Make in India' and will boost the Navy's might.
It underwent around 120 days of extensive sea trials and tests for various equipment, an official earlier 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 first Kalvari, commissioned on December 8, 1967, was also the first submarine of the Indian Navy. It was decommissioned on May 31, 1996 after nearly three decades of service.
Kalvari is named after the dreaded tiger shark, a deadly deep sea predator of the Indian Ocean.