The prime minister's special aircraft touched down at Vnukovo International airport here amid a cloudy day with the temperature at 5 degrees Celsius, but bitterly cold.
He was received by Russian Deputy Foreign Minister Mikhail Bogdanov.
Both sides are set to ink six agreements, including one on the transfer of sentenced persons and on science and technology, during their annual summit Monday.
Earlier, before leaving on the visit, the prime minister had described the annual summit he would hold with Russian President Vladimir Putin on Monday as an "important feature of our special and privileged strategic partnership".
He said India's scope of ties with Russia is "unique, encompassing strong and growing cooperation in areas such as defence, nuclear energy, science and technology, hydrocarbons, trade and investment and people to people exchanges".
He said he would convey to President Putin "the importance we attach to our relations with Russia, and I will use this visit to strengthen our partnership in every possible way".
Despite the high expectations ahead of the visit, India and Russia are not to ink the commercial agreement on the third and fourth reactors for Kudankulam.
The two leaders are set to go over the main pillars of the bilateral strategic partnership, including defence, energy, space, science and technology, economy.
Manmohan Singh would be conferred an honorary doctorate by Moscow State Institute of International Relations, which he said is a "testimony of the relations between our two countries".