Mr Leonov was born in 1934 in a large peasant family in western Siberia. The mission is credited with kick-starting eventual global cooperation aboard the worldwide Space Station.
Leonov made history in 1965 by exiting his capsule for 12 minutes, Russia Today reported. The Russians beat the Americans there, too. From left to right, Alexey Leonov, Charles Conrad Jr. "I can still hear my breath and my heartbeat in that silence".
Spacewalking always carries a high risk but Mr Leonov's pioneering venture was particularly nerve-wracking, according to details of the exploit that only became public decades later.
Unknown to mission control back home, he took the unsafe step of using a valve to release oxygen from his suit, a risky move since it could starve him of air he needed to survive. Taking a hair-raising decision, he opened a valve on the suit to let enough air escape for him to enter the airlock.
Leonov trained as a military pilot before becoming a cosmonaut.
Koch, who is seven months into her space flight, will set out on the first ever female spacewalk on Monday, October 21 after the first attempt was called-off due to spacesuit issues.
The short foray, a significant advance in the space race between the Soviet Union and the United States, was no easy task, and not without its mishaps.
He also was the Soviet commander of the Apollo-Soyuz joint space mission in 1975, a prelude to the worldwide co-operation seen aboard the current space station.
The cosmonaut was well known for his humour. The détente-inspired mission saw the last Apollo spacecraft rendezvous in space with a Soviet Soyuz, as a demonstration of supposedly thawing US-Soviet relations. "We should collaborate and work together".
Oleg Kononenko and Alexei Ovchinin, two members of the International Space Station, dedicated their spacewalk on May 29 to Leonov, who celebrated his 85th birthday the following day.
Leonov's wife, however, did not comment on the reports, saying simply that "this isn't the time".
When his crew returned to earth at the end of June, Leonov was already unwell.
"This is a loss for the whole planet", said Russian cosmonaut Oleg Kononenko.
Alexi Leonov was one of the greats in spaceflight.
Messages of condolences poured in from around the globe following news of his death.
Leonov handed away in Moscow on Friday morning, aged 85.