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The deal - announced in the Indian capital Delhi - has now to be ratified by the Indian Government.
The aircraft carrier, the Admiral Gorshkov, is a 29-year-old ship which the Russians took out of service in 1994.
The deal has been criticised over the years by some who feel too much is being spent for a relatively old ship.
But India's navy chief, Admiral Madhvendra Singh, defended the purchase saying the life of an aircraft carrier was 40 years.
"After repair and refitting, the Admiral Gorshkov will be 70% new.
"We have got a very, very fine deal," he said.
The 44,000 tonne carrier was commissioned into the Russian Navy in the late 80s.
Reports say India wants the ship refitted to enable it to carry MiG-29 fighter aircraft.
Defence partners
Russia is India's largest supplier of military hardware and military co-operation is an important part of the relations between the two former Cold War allies.
The first joint naval exercises since the break-up of the Soviet Union were held this summer.
Designers from both the countries are also working on a joint fighter jet.
But recently India has also been sourcing supplies and equipment from other countries, most notably France and Israel.
And Britain's BAE Systems recently won a $1.7bn contract to supply India with jet trainer aircraft.
India's long-time rival Pakistan has expressed its concern over these purchases, saying it feared it would lead to an arms race in South Asia.