The Soyuz capsule docked at 22:48 GMT Saturday, just six hours and 20 minutes after blasting off from Russia’s launch complex in Baikonur, Kazakhstan, The Associated Press reported.
The launch took place on the 50th anniversary of the day US astronauts landed on the Moon.
The capsule is carrying Andrew Morgan of the United States on his first spaceflight, Russian Alexander Skvortsov on his third mission to the space station and Italian Luca Parmitano.
They will join Russian Alexey Ovchinin and Americans Nick Hague and Christina Koch who have been aboard since March.
The crew patch for the expedition echoes the one from Apollo 11′s 1969 lunar mission.
'Lucky and privileged'
Speaking at a prelaunch news conference in Baikonur, Parmitano, 42, said the crew were "lucky and privileged" to have their launch coincide with the Apollo 11 date, and indicated that they were wearing badges honoring the anniversary.
Morgan paid tribute to the Apollo 11 landing as a "victory for all of mankind" but ducked a question on whether Russian cosmonauts would ever reach the Moon — the Soviet Union only ever sent unmanned missions there.
NASA was "even more capable" of accomplishing great things when it did so "as part of an international cooperation," Morgan said.
Five decades after the 1969 Moon landing, Russia and the West are still competing in space, even if the emphasis is on cooperation at the ISS.
NASA no longer operates manned flights to the ISS leaving it wholly dependent on Roscosmos' Soyuz program.
But in recent times private companies like SpaceX and Boeing have bid to end the Russian monopoly on manned launches to the ISS, winning multi-billion contracts with NASA.