"A tribute to Leonov as today is a spacewalk", Mission Control in Houston said.
Russian space agency Roscosmos announced Friday that Leonov has died in Russia at the age of 85. On March 18, 1965, he embarked on the first spacewalk, spending 12 minutes outside the Voskhod 2 capsule.
Russian President Vladimir Putin sent his condolences to Leonov's loved ones, Kremlin spokesman Dmitry Peskov said.
Stanley Kubrick's 1968 film "2001: A Space Odyssey" included recordings of Leonov's breathing in space.
On the Apollo-Soyuz mission in 1975, Leonov met with USA astronauts in space and gave TV viewers tours of their respective crafts, the first time Soviet and U.S. cosmonauts collaborated in space.
Days before his 85th birthday in May, two Russian crew members on the International Space Station ventured into open space on a planned spacewalk with stickers attached to their spacesuits paying tribute to Mr Leonov, and congratulated him from space.
Leonov was born in 1934 in the former Soviet Union.
This came as the Soviet Union and United States, Cold War foes, were locked in a frantic race to conquer space.
Nasa broke into its live televised coverage of a spacewalk by two Americans outside the International Space Station to report Mr Leonov's death. Apollo-Soyuz 19 was a prelude to the worldwide cooperation seen aboard the current global Space Station.
British astronaut Tim Peake said Mr Leonov was "a hero to so many, pioneer of spacewalking and always full of wisdom and humour".
Two NASA astronauts are now outside the International Space Station on the second of several planned spacewalks to replace batteries affixed to the outside of the spacecraft.
Nasa on Friday offered its sympathies to Leonov's family, saying it was saddened by his death.
"This is a loss for the whole planet", said Russian cosmonaut Oleg Kononenko. Two NASA astronauts are conducting one Friday outside the ISS to install new batteries.
"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.