Nespoli is part of a trio of astronauts from the United States, Russia and Italy involved in the mission, which marks a step toward boosting US research projects aboard the orbiting laboratory.
The rocket carrying the three spaceflight veterans lifted off at 5:41 pm central European time from the Baikonur Cosmodrome in Kazakhstan.
The men will join three crew members already aboard the station, a lab costing 150 billion USD and located about 400 kilometres above Earth.
Their arrival marks the first time that NASA has four crew members instead of three available for medical experiments, technology demonstrations and other research aboard the station.
Nespoli is making his third space flight in 10 years, having previously served on both space shuttle and space station crews.
“Beam me up Soyuz! Hitching another ride soon to the @Space_Station with @AstroKomrade & @Ryazanskiy_ISS #VITAMission #Exp52_53,” the European Space Agency (ESA) astronaut wrote on Twitter before takeoff.
The tweet featured a video of Nespoli is his space suit entitled “Let's do this!”
The men are scheduled to return to Earth in December.