It was only Putin's second trip abroad since the coronavirus pandemic began -- he skipped both the G20 and COP26 summits this year -- and comes after a June summit with US president Joe Biden in Geneva.
"We perceive India as a great power, a friendly nation and a time-tested friend," Putin said in the Indian capital alongside Modi.
Russia has long been a key arms supplier to India, which is looking to modernise its armed forces, and the S-400 missile system is one of their most high-profile current contracts.
"Supplies have begun this month and will continue," Indian foreign secretary Harsh Vardhan Shringla said after the summit.
The deal is worth over $5 billion and was first signed in 2018, but it threatens to upend the burgeoning relationship between New Delhi and Washington.
The United States has warned of sanctions under the Countering America's Adversaries Through Sanctions Act (CAATSA), which is aimed at reining in Russia, and the State Department said last week that no decisions had been made on any waivers for India.
"Our Indian friends clearly explained that they are a sovereign country and that they will decide whose weapons to buy and who will be India's partner," Kremlin spokesman Dmitry Peskov told reporters on Monday.
India was close to the Soviet Union during the Cold War, a relationship that has endured, with both calling it a "special privileged strategic partnership".
Putin's visit was "hugely symbolic", said Nandan Unnikrishnan from the New Delhi-based Observer Research Foundation think tank.
"There has been a lot of speculation about the nature of the India-Russia relationship and whether it is fraying because of Russia's closeness with China and India's with the US, but this visit puts all that to rest."
In its efforts to address a rising China, Washington has set up the QUAD security dialogue with India, Japan, and Australia, raising concerns in both Beijing and Moscow.
Putin's visit comes in the shadow of complex regional dynamics, with tensions mounting between New Delhi and Beijing, traditionally an ally of Moscow, following deadly clashes in a disputed Himalayan region.
"Russia's influence in the region is very limited," said Tatiana Belousova of OP Jindal Global University in Haryana, "mostly because of its close ties with China and unwillingness to act in dissonance with the Chinese regional interests."
'New order evolving'
Talks were dominated by defence and energy issues, with the boss of Russian energy giant Rosneft, Igor Sechin, also attending as a "number of important energy agreements" were on the table.
Rosneft said in a statement it will supply of up to two million tonnes of oil to India through the Black Sea port city of Novorossiysk in southern Russia.
New Delhi has long sought to diversify its military imports but analysts believe it could take some time before it moves away from Russia.
The 10-year defence agreement signed Monday showed both the strength of its ties with Russia "and the difficult path India has to traverse to diversify its arms suppliers and develop its indigenous production capacity," Unnikrishnan said.
India is also keen to increase domestic production and has launched a joint venture with Russia to manufacture AK-203 assault rifles.
Kalashnikov Concern said Monday that it had agreed on a contract to supply more than 600,000 AK-203 assault rifles manufactured in India for the Indian defence ministry.
"We are ready to start production of modern AK-203s ... within the next few months," said general director Vladimir Lepin.
India and Russia normally hold annual summits, but the leaders' last in-person meeting was on the sidelines of the 2019 BRICS Summit in Brazil.
Putin's visit "reiterated the importance of this moment when a new order is evolving and that together they have a better chance of shaping it," Samir Saran of the Observer Research Foundation told AFP.
The two countries' foreign and defence ministers held talks Monday ahead of Putin's arrival.
Moscow and New Delhi hold "identical or near-identical positions on the most important global and security issues", said Russian foreign minister Sergei Lavrov.