Hague and Gorbounov will spend around five months on the ISS and, until then, carry out around 200 scientific experiments. When they return to Earth, they will be joined by Wilmore and Williams.
The two NASA astronauts traveled to the space station in early June aboard Boeing's CST-100 Starliner capsule.
The spacecraft developed a helium leak even before launch, a problem that repeated itself again on its journey to the ISS.