The Kremlin said before the two-day visit that the "key feature" would be the signing of a $5-billion deal for the advanced S-400 air defence system, despite US sanctions against countries buying Russian defence hardware.
India will ask the United States for a special waiver for the purchase -- as discussed by their defence and foreign ministers in New Delhi last month -- but Washington has signalled there is no guarantee it will accede.
The US is in a difficult position as it seeks to contain China through better ties with India, which like Washington has been unnerved by Beijing's growing assertiveness.
Russia, India to sign deal on S-400 air defence systems this week: Kremlin
Washington and New Delhi announced plans last month for joint military drills in 2019, and agreed on the exchange of sensitive military information.
But Russia remains India's main arms supplier, and a string of new deals with the Asian giant would be a major win for Moscow -- and a big snub to the US.
Putin and Modi, who appear to enjoy a personal rapport, are also likely to discuss a deal for four Krivak-class frigates worth $2 billion and 200 light utility Ka-226 helicopters pegged at $1 billion.
India and Russia have already concluded an Inter-Governmental Agreement for the choppers, 60 of which would be built in Russia and the rest in India.
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"Russia is a time-tested friend. I am really glad some spine has finally been shown by India," RR Subramanian, a Delhi-based strategic affairs analyst, told AFP.
"It's about time we... showed that we are not going to be pushed around by Washington."
Experts say India needs the sophisticated S-400 system to fill critical gaps in its defence capabilities, in view of China's rise and perceived threats from Pakistan, against whom India has fought three wars.
Indian Air Force Chief Birender Singh Dhanoa said on Wednesday that the S-400 and the 36 Rafale fighter jets purchased from France -- a 2016 deal mired in political controversy -- represent a "booster dose" for the country.
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Putin, 65, and Modi, 68, are also set to discuss a possible second Russian-built nuclear power plant in India. Moscow is currently expanding India's biggest nuclear power plant in Kudankulam.
Also on the agenda is Russian training for Indian astronauts as New Delhi aims to launch its first crewed space mission in 2022.
Rakesh Sharma, the only Indian to travel in space, did so on a Soviet spacecraft in 1984.
But military kit is the main focus.
India is the world's biggest arms importer and is undergoing a $100-billion upgrade of its ageing hardware, much of it of Soviet vintage like MiG jets that regularly crash in the Indian countryside.
Russia is still India's biggest arms supplier, and the two have had warm ties since Stalin died in 1953.
The US is now number two, though, supplying the Indian military with advanced hardware like Apache attack helicopters and negotiating the sale of armed drones.
Russia-India trade has slipped below $10 billion since 2014, as Modi has cultivated closer diplomatic and economic ties with Washington, while Russia has courted Pakistan and China.
But ties received a boost last year when Modi and Putin held a fruitful annual bilateral summit, followed by meetings in Astana and at the G20 in Germany. They also met in Sochi this year.
On the strategic front, Russia helped India become a full member of the Shanghai Cooperation Organisation this year and has backed New Delhi's long-held demand for a permanent UN Security Council seat.
Moscow is also pushing for India's entry into the Nuclear Suppliers Group of countries controling access to nuclear technology despite atomic-armed India not signing the Nuclear Non-Proliferation Treaty (NPT).
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