"At 5:44 am Moscow time (01:44 GMT), the manned Soyuz TMA-13M spacecraft docked successfully with the ISS," the Russian space agency Roskosmos said in a statement.
German Alexander Gerst from the European Space Agency, Russian cosmonaut Maxim Surayev and his NASA colleague Reid Wiseman opened the hatch into the ISS just over two hours later, Russian mission control said on its website.
Grinning broadly, they hugged the crew of three already on board the international space laboratory, US astronaut Steve Swanson and Russians Alexander Skvortsov and Oleg Artemyev.
The Soyuz craft had blasted off from Russia's Baikonur cosmodrome in Kazakhstan on schedule shortly before midnight Moscow time.
The astronauts took a six-hour fast-track route to the ISS after the previous crew to travel to the ISS in March was forced to spend two days in orbit due to a technical glitch.
The new ISS crewmembers are due to carry out a mission lasting 167 days and return to Earth in November.
Gerst, 38, is on his first space mission. During his six-month stay he is expected to work on some 100 experiments. Surayev, 42, is on his second lengthy ISS mission after his maiden voyage in 2009, when he became the first Russian space blogger.
During a press conference on Wednesday, the crew was asked whether the current tensions between Russia and the West over Ukraine would affect their relationship. They responded by hugging each other.
Since the retirement of the US space shuttle in 2011, NASA is for now wholly reliant on Russia for delivering astronauts to the space station on its tried-and-trusted Soyuz launch and capsule system.
The recent chill in East-West relations set off by the crisis in Ukraine has prompted Russia to warn that it may prohibit the United States from using one of its newest rockets in the launch of American military satellites.
Moscow has also hinted that it may turn down Washington's request to extend the lifespan of the ISS by four years through 2024.
Russian Deputy Prime Minister Dmitry Rogozin, who oversees the space sector, said this month that Russia will only need the ISS until 2020, saying that Russia wanted to use its resources on "more promising projects."
NASA for its part cut ties with Russia last month, except for cooperation aboard the ISS due to Moscow's role in Ukraine.
"Given Russia's ongoing violation of Ukraine's sovereignty and territorial integrity, NASA is suspending the majority of its ongoing engagements with the Russian Federation," NASA said in a statement.
Rogozin responded by derisively suggesting that NASA might have to use a "trampoline" to send its astronauts to the ISS.
In all 16 countries are participants in the ISS programme, though the US and Russia do the lion's share of financing the project.