The Soyuz rocket carrying Fyodor Yurchikhin, Karen Nyberg and Luca Parmitano lifted away from the Baikonur Cosmodrome at 02:31 local time on Wednesday (20:31 GMT Tuesday).
Georgian Yurchikhin and American Nyberg have both been into space before. Italian Parmitano is a first-timer.
They arrived at the orbiting platform five hours and 46 minutes later.
Their Soyuz capsule was using a new flight profile that dramatically reduces the rendezvous time from the traditional two days.
Reducing time to reach the ISS from 2 days to under 6 hours is quite radical.