The docking took place smoothly Friday and the crew entered the space laboratory after a lengthy procedure to open its hatches.
The mission is set to last four months.
The crew consists of two astronauts from the Russian space agency Roscosmos, Sergey Ryzhikov and Andrey Borisenko, as well as NASA astronaut Shane Kimbrough.
They join American Jeff Williams and Russians Oleg Skripochka and Alexey Ovchinin, who are already aboard the space station.
The new arrivals are carrying the relics of Seraphim of Sarov, an 18th century saint, provided by the Russian Orthodox Church.