Putin will hold talks with Modi after arriving in the Indian tourism state of Goa for a BRICS summit also involving the heads of leading emerging nations Brazil, China and South Africa.
Among the agreements expected to be signed between the two leaders are Moscow's delivery of its most advanced anti-aircraft defence system to India.
India, the world's top defence importer, is undergoing a $100-billion upgrade of its Soviet-era military hardware, as it looks to protect its borders from arch-rival Pakistan and an increasingly assertive China.
Modi and Putin will also focus on strengthening energy ties to meet India's growing thirst for fuel and electricity for its fast-growing economy.
India expresses disappointment over Pakistan-Russia military cooperation
Russia's biggest oil company Rosneft is expected to acquire India's Essar Oil in a multi-billion-dollar deal, according to local media reports, quoting officials involved in the agreement.
"The menu is vast," India's ambassador to Russia, Pankaj Saran said at a briefing on the talks, without detailing the deals to be signed.
"It is more than a relationship, it is a partnership and very justifiably it has been described by the two leaders as both special and privileged, as well as of course strategic," he said.
"It is very deep and very intense and it is poised to grow even further."
Saran said he also expected them to discuss India's tensions with neighbour Pakistan, which spiked after last month's attack on an Indian army base that killed 19 soldiers.
Modi has sought to isolate Pakistan internationally since the attack that India blamed on Pakistan-based militants.
India said it subsequently carried out strikes against militants over the border in Pakistan, prompting a furious response from Islamabad.
"We have conveyed our views to the Russian side. We are confident that Russia will reflect upon our concerns," Saran said.
But Putin is seen as unlikely to weigh into the dispute between the rivals, as Moscow also eyes closer defence ties with Islamabad. Russia and Pakistan carried out their first joint military exercise last month.
In beachside Goa, the two leaders will reach agreement on Moscow's delivery of the S-400 Triumph defence system, Russian news agencies quoted a Putin aide as saying on Friday, without detailing a timeframe.
The S-400 is Russia's most modern air defence system and has been deployed to Syria, where Moscow is conducting a bombing campaign in support of President Bashar al-Assad, its long-time ally.
India's Modi hosts BRICS leaders as bloc beset by economic woes
India was the erstwhile Soviet Union's closest military ally during the Cold War and a major importer of its military hardware. But in recent years Delhi has turned to the United States for supplies, as the two nations forge stronger ties.
Modi will also hold bilateral meetings with other BRICS leaders including China's President Xi Jinping late Saturday, before hosting a dinner in their honour to officially start the BRICS summit.
The BRICS leaders will get down to talks on Sunday, with enhancing trade ties along with "regional and global terrorism" issues that are expected to be on the agenda.
BRICS was formed in 2011 with the aim of using its growing economic and political influence to challenge Western hegemony.
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