During their stay, in which they are rotating in to replace departing crew, some 200 scientific experiments are scheduled to be carried out.
The quartet blasted off from Florida late Sunday aboard a SpaceX Falcon 9 rocket.
The capsule docked with the ISS and its hatch was opened at 3:50 am Tuesday US eastern time (0850 GMT), with the smiling new arrivals hugging their colleagues as they entered, a live feed of the docking showed.
This is the eighth standard ISS crew rotation mission performed by SpaceX for the US space agency NASA, reflected in the mission name: Crew-8.
American Michael Barratt is the only Crew-8 astronaut to have already visited the space station. The ISS stay is the first for Americans Matthew Dominick and Jeanette Epps, and Russian Alexander Grebenkin.
They join seven crew already on board the ISS.
After a transition period of a few days, the four members of Crew-7 — from Denmark, Japan, Russia and the United States — will return to Earth aboard another SpaceX capsule.
NASA and Russian space corporation Roscosmos, which jointly operate the ISS, have established an astronaut exchange program, each taking turns to send crew members to the outpost.
The program has been maintained despite deep tensions over the war in Ukraine, and the ISS is now one of the few areas of cooperation between Washington and Moscow.
© Agence France-Presse