On March 18, 1965, when there were still many unknowns about whether a person can survive in the space, he went out of his spacecraft and proved that it is achievable, spending 12 minutes floating outside.
He flew in space a second time in 1975, as part of the historic Apollo-Soyuz mission, the first US-Soviet space flight, which occurred as the two superpowers were pursuing a policy of detente during the Cold War.
Though less well known internationally than Yuri Gagarin, the first man in space, Leonov was a household name in his native Russian Federation and will be remembered in particular for his role in the 1965 Voskhod-2 mission.
Leonov died at Moscow's Burdenko hospital on Friday after a long illness, his assistant confirmed.
Russian space agency Roscosmos Space Corporation announced his passing Friday.
Leonov and one other cosmonaut, pilot Pavel Belyayev, (codenames Almaz-1 and Almaz-2) have been rocketed almost 500 kilometres (310 miles) into orbit. He was a friend of Yuri Gagarin, who became the first man in space in 1961 and trained with him.
Leonov attended several anniversary commemorations of the Apollo 11 moon landing as a guest of NASA.
Alexei Leonov was the first man to walk in Space from Voshkod 2.
"His venture into the vacuum of space began the history of extravehicular activity that makes today's Space Station maintenance possible", NASA said on Twitter.
Russian cosmonaut Oleg Kononenko said Leonov's death was a "loss for the whole planet", while President Vladimir Putin said he admired the astronaut's courage.
Soyuz-Apollo was the first Soviet-American joint space mission in history.
Just the previous month an unmanned mission to test.
The cosmonaut was well known for his humour.
"Alexei is a unique person", she informed AFP.
Leonov is to be buried on Tuesday at a military memorial cemetery outside Moscow, Roscosmos said.