Fire from the boosters of the Soyuz TMA-19M rocket cut a bright light through the overcast sky at the Russia-operated cosmodrome in Kazakhstan, after the spacecraft launched on schedule at 1103 GMT, according to live television broadcasts.
A spokesman for Mission Control confirmed to AFP that the launch had gone according to plan.
They are due to dock at the ISS about six hours later.
“It was great to watch Tim Peake blast off on his mission to join the International Space Station,” British Prime Minister David Cameron said on Twitter.
Former army major Peake — a European Space Agency flight engineer — begins a mission of more than 170 days or nearly six months at the orbiting research outpost along with Russia’s Malenchenko and NASA’s Kopra.
His two fellow crew members have already spent 641 and 58 days in space respectively.
Peake’s mission has generated considerable excitement in Britain, where the government unveiled an ambitious new Space Policy on the eve of his departure for the International Space Station.
The policy aims to more than triple the value of the sector to the national economy, reaching USD 40 billion by 2030.
The Soyuz trio will join up with the three astronauts already at the ISS — Scott Kelly of NASA and Russians Sergei Volkov and Mikhail Kornienko, and begin work on Expedition 46.
Three other astronauts – NASA’s Kjell Lindgren, Japanese astronaut Kimiya Yui and Russian cosmonaut Oleg Kononenko — returned to Earth on Friday in a rare nighttime landing, marking the end of Expedition 45.
The ISS space laboratory has been orbiting the Earth at roughly 28,000 kilometres per hour since 1998.
Space travel has been one of the few areas of international cooperation between Russia and the West that has not been wrecked by the Ukraine crisis.