On March 18, 1965, he embarked on the first spacewalk, spending 12 minutes outside the Voskhod 2 capsule.
Though Leonov wasn't the first man on the moon (a goal he wasn't shy about), he earned his own "first" in the space race between the United States and Soviet Union.
Leonov flew a second time in 1975, when he was the commander of the Soviet half of the landmark Apollo-Soyuz test project, the first Russian-American joint space mission.
"A tribute to Leonov today is a spacewalk", Mission Control in Houston said.
The flight and spacewalk were successful on the whole, but his return to Earth almost ended in tragedy when Mr Leonov and another cosmonaut, Mr Pavel Belyayev, crash-landed in the Siberian woods.
Leonov might have become the Soviet Union's first moonwalker, in fact, had his country's lunar-landing effort not been cancelled in the wake of Apollo 11's triumphant moon landing by Neil Armstrong and Buzz Aldrin on July 20, 1969.
Leonov was a close friend of Yury Gagarin, who became the first human to go to outer space in 1961.
British astronaut Tim Peake said Mr Leonov was "a hero to so many, pioneer of spacewalking and always full of wisdom and humour".
"Putin always admired Leonov's courage and thought he was an extraordinary man", Peskov told Russian news agencies.
"We had this tradition that he would give cosmonauts pep talks before they board the spacecraft", Kononenko said.
NASA paid tribute to Leonov on Friday.
On Twitter, Nasa added: "His venture into the vacuum of space began the history of extra-vehicular activity that makes today's Space Station maintenance possible".
Leonov became a legend at home and his feats were immortalised in cinema and literature.
The late science fiction writer Arthur C. Clarke named a Soviet spaceship after him in his "2010" sequel to "2001: A Space Odyssey".
The 1965 mission was also celebrated in a 2017 Russian film "The Spacewalker" where Leonov acted as consultant.
"One of the first cosmonauts of the world space era, Alexei Leonov was committed to his Motherland and his cause, his name is lettered in gold in the world space exploration history", Roscosmos said.