Nasa broke into its live televised coverage of a spacewalk by two Americans outside the International Space Station to report Mr Leonov's death.
Soviet cosmonaut Alexei Leonov, who made history in 1965 by becoming the first person to ever walk in space, died on Friday in Moscow, the TASS news agency reported, citing his aide Natalya Filimonova.
Leonov's feats were immortalised in cinema and literature.
Leonov's spacewalk preceded the first U.S. one, by Ed White, by less than three months.
Born in Siberia, the youngest of eight children, Leonov became a fighter pilot before being selected as one of the first potential cosmonauts.
Space station crew members have conducted 220 spacewalks in support of the assembly and maintenance of the orbiting laboratory, spending a total of 57 days, 13 hours and 12 minutes working outside the station.
Leonov's 12-minute spacewalk on March 18, 1965, preceded the first US spacewalk by Ed White by less than three months.
Though not as well known around the world as the first man in space, Yuri Gagarin, Leonov was a household name in Russian Federation. He was such a legend that the late science fiction writer Arthur C. Clarke named a Soviet spaceship after him in his 2010 sequel to 2001: A Space Odyssey.
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Leonov was also supposed to be the first man to land on the moon.
In 1975, he also took part in the historic Soyuz-Apollo spaceflight, which signalled the end of the Space Race.
The cosmonaut turned 85 in May.
Former Russian cosmonaut Alexei Leonov in 2010. Leonov is two time Hero of the Soviet Union.
Leonov was an accomplished artist and writer and his contemporaries described him as warm and likable.
"Alexei is a unique person", she told AFP.
Leonov's funeral will be held next Tuesday at the Federal Military Memorial Cemetery in the Russian capital.