Russia’s Roscosmos space agency said that the Soyuz MS-06 spacecraft “successfully docked” at the ISS at 0255 GMT in a statement on its website.
The Soyuz rocket carrying Alexander Misurkin of Roscosmos, NASA first-time flyer Mark Vande Hei and his veteran colleague Joe Acaba launched as scheduled from Baikonur at 3:17 am (2117 GMT).
The trio will now join Paolo Nespoli of Italy, Sergey Riazanski of Russia and Randy Bresnik of the US aboard the orbital lab.
The launch marked the first time two US astronauts have blasted off together on a mission to the ISS from Russia’s Baikonur since June 2010.
The American space agency stopped its own manned launches to the ISS in 2011 but recently moved to increase its crew complement aboard the ISS as the Russians cut theirs in a cost-saving measure announced last year.
Acaba, 50, has spent nearly 138 days in space over two missions, while Vande Hei, 50, served with the US army in Iraq before training as an astronaut.
Misurkin, 39, who is beginning his second mission aboard the ISS, also has a military background.
Speaking at the pre-launch news conference on Monday, Acaba, who is of Puerto Rican heritage, said he would be taking some “musica Latina” on board to lift his crewmates’ spirits.
“I can guarantee my crewmates they will not fall asleep during that music and if you want to dance at about 3 am tuned into our Soyuz capsule I think you’ll enjoy it,” he told journalists.
‘Praying for people’
The launch has been overshadowed by deadly storms that have battered the Caribbean and the southern half of the United States.
External cameras on the ISS captured footage of hurricane Irma last week brewing over the Atlantic as it prepared to wreak deadly havoc.
NASA’s Johnson Space Center in Houston said earlier this month it suffered “significant” damage during Hurricane Harvey, although Mission Control remained operational.
Vande Hei struck a sombre note in a pre-launch tweet on Monday.
“L-2 days. Sunrise over Baikonur, Kazakhstan. Praying for the people of Florida as well as the continued recovery of the Texas Gulf Coast,” he said.
Space is one of the few areas of international cooperation between Russia and the US that has not been wrecked by tensions over the conflicts in Ukraine and Syria.
The ISS orbits the Earth at a height of about 250 miles (400 kilometres), circling the planet every 90 minutes at a speed of about 17,500 miles (28,000 kilometres) per hour.