The Russian space agency Roscosmos said it was saddened to announce the death of "cosmonaut No 11" who was twice decorated with the country's top honor, the Hero of the Soviet Union.
Leonov was a close friend of Yury Gagarin, who became the first human to go to outer space in 1961.
Earlier this year, two Russian cosmonauts honored Leonov on his 85th birthday. They wore placards on their spacesuit backpacks, one saying "Leonov No. 1" and the other "Happy Birthday, Alexey Arkhipovich."
Leonov chalked up one of Russia's major space triumphs on March 18, 1965, when he ventured outside his Voskhod 2 spacecraft to carry out history's first spacewalk.
Connected to the Voskhod by an 18-foot-long tether, Leonov spent 12 minutes floating outside before struggling to get back inside his spacecraft. In the vacuum of space, his suit had ballooned to the point that it would not fit through the hatch. After opening a valve to bleed off pressure, Leonov finally managed to squeeze back inside.
NASA astronaut Ed White became the first American spacewalker three months later.
In 1975, Leonov took part in the historic Soyuz-Apollo spaceflight which, put an end to the "space race" between the U.S. and Soviet Union.