The head of the Indian navy, Adm. Nirmal Verma, commissioned the vessel into active service as India's 140th warship.
The Satpura, which follows the Shivalik into service, is the second of three Project 17 stealth frigates being built by Mazagon Dock in Mumbai.
It will be followed by the Sahyadri early next year.
The vessels are based on the three 4,100-ton Talwar-class frigates that Russia built for the Indian navy a decade ago. However, the officially termed guided-missile stealth frigates come in at 6,200 tons.
The Satpura carries 24 Russian Klub missiles with a range of around 130 miles.
The navy originally wanted the Indian-made Brahmos missile but it was too heavy for the vessel, the Business Standard report said. Only India's heavier destroyers are armed with the Brahmos.
The Satpura has an Israeli Barak air defense system and an RB-6,000 multi-barreled depth charge launcher. It also carries two Sea King, or indigenous Dhruv helicopters.
Power for the 465-foot warship is provided by two French Pielstick diesel engines. In addition, two General Electric LM-2500 gas turbines are used in tandem with the diesels for bursts of speed.
The stealth aspect comes in its design, configured to reduce its radar, infrared, electronic, acoustic and visual signatures, the report said.
Similar designs are being used in Project 28, the construction program for anti-submarine corvettes that are being built at Garden Reach Shipbuilders and Engineers in Kolkata.
Construction cost for the stealth frigates has been kept down through the use of warship-grade steel from the Indian firm Essar Steel, rather than importing similar grades.
But India remains concerned over the amount and cost of foreign high-tech equipment in its new vessels, Verma said.
Vice Adm. Ganesh Mahadevan, the navy's chief of Materials, said indigenization will rise dramatically for future vessels starting next year.
The Ministry of Defense also announced that the navy, along with the air force, is on schedule to receive additional Hawk AJT trainer jets.
The navy will get 17 of the 57 trainers to be built by state-run Hindustan Aeronautics.
Delivery of the first aircraft of the 57 will start in 2013 and be finished by 2016.
The $700 million order for the 57 two-seat aircraft was signed with HAL in July 2010, a report on the Machinist.in Web site said.
The air force is getting the other 40 Hawks, an advanced trainer designed by BAE Systems and which can be used as a low-cost fighter.
The order for the 57 from HAL comes after a previous contract with BAE and HAL for 66 Hawk aircraft.
In March 2004, the government signed a contract with BAE Systems and Rolls-Royce Turbomeca UK for the purchase of 24 Hawk AJTs to be built in the United Kingdom.
Also agreed at the same time was for HAL in Bangalore to manufacture another 42 Hawks under a transfer of technology contract, Defense Minister A.K. Antony said in the upper house of Parliament.