Here is Your 10-point Cheat-Sheet to This Story:
Mr Hagel's trip follows one by US Secretary of State John Kerry last week and is part of the build-up to PM Modi's talks with President Barack Obama in Washington in September.
His trip comes as India is considering a $1.4 billion deal to buy at least 22 US Apache and 15 Chinook helicopters, both built by Boeing.
The US Defence Secretary described India as a country that will help shape a "new world order" that is emerging in this century.
The US is to persuade India into a follow-on order of 39 AH-64D Apache helicopters in addition to the 22 now being negotiated. The two sides have been wrangling over the price of the gunships, with the initial deal having been estimated to be worth $1.4 billion.
The initial batch of Apache helicopters is meant to replace the Indian Air Force's ageing fleet of Soviet-era aircraft and will be armed with Hellfire and Stinger missiles.
The Indian Army has separately requested a fleet of at least 39 of these attack aircraft, some of which will be deployed as part of a new mountain strike corps it is raising along the disputed border with China, an army official said.
The two sides are also in talks to finalise a contract for the Indian Air Force to buy 15 CH-47F Chinooks, a twin-rotor helicopter capable of lifting heavy loads.
The cabinet has just cleared a proposal to allow 49 percent foreign participation in the defence industry, up from a current cap of 26 percent, in a bid to boost local manufacturing and end a long dependence on overseas acquisitions that made India the world's biggest arms importer in recent years.
The PM and Mr Hagel discussed the US decision to go ahead with limited airstrikes in ISIS-controlled areas in Iraq. India has vital stakes in the region. They also spoke of the situation in Afghanistan. India has voiced concern about the instability in Afghanistan as the United States prepares to withdraw its troops.
The United States is also keen to secure greater military cooperation with India as it seeks to counter the growing Chinese firepower in Asia. Mr Hagel said the purpose of his visit went beyond arms sales. "We need partners. We need relationships. That's the kind of world we live in, and that's the kind of world that we're going to be living in."
PM Modi To Visit US For Quad Summit, Attend UN Assembly From September 21-24 True Secular, Liberal And Feminist: Kangana Ranaut Praises PM Modi "Congress Ecosystem Is Angry": PM On Ganesh Puja At Chief Justice Home 9 Dead, 2,800 Hurt As Pagers Explode Across Lebanon, Hezbollah Blames Israel 'Pager Bombs' Target Hezbollah In Lebanon. What We Know So Far - 5 Points IndiGo Flight Tailstrike Leaves Huge Dent During Take-Off From Delhi Airport World's Oldest Sunday Newspaper, 'The Observer', Up For Sale PM Modi To Visit US For Quad Summit, Attend UN Assembly From Sept 21-24 Ground Report: Central Forces' Canteens Open To Public In Violence-Hit Manipur Track Latest News Live on NDTV.com and get news updates from India and around the world.