The Russian rocket launched from the Baikonur Cosmodrome in Kazakhstan in front of the world’s media following weeks of preparation.
Major Peake, 43, is making history as the first fully British professional astronaut to be employed by a space agency.
Images of the launch showed the trail of flames the rocket left in its wake as it sped up into the blue sky, before it became a tiny speck in the distance.
A view inside the capsule showed the astronauts in spacesuits as the rocket lifted off. Maj Peake could be identified by the Union flag on his sleeve. He smiled at the camera, waved and gave a thumbs up as they sat back in their seats for the trip into space.
The rocket blasted off from Launch Pad 1, the historic spot from which Yuri Gagarin launched to become the first man in space in April 1961.
It was due to take the crew eight minutes and 48 seconds to reach orbit following take-off from Baikonur ahead of the six-hour trip to the ISS where they will spend the next five and a half months.
The Soyuz FG rocket was packed with 300 tonnes of fuel.
Earlier there were emotional scenes as Maj Peake said goodbye to family and friends, including his wife, Rebecca, and two sons, Thomas, six, and Oliver, four.
Well-wishers gathered waving Union Flags, cheering and shouting “Go Tim” as Maj Peake and his two crew companions departed from the Cosmonaut Hotel for their flight.
In his final message to Twitter followers, Maj Peake said: ‘’Last tweet before launch – Go for flight! Thanks for all the good luck messages – phenomenal support!’’
And the UK Space Agency tweeted pictures of the astronaut signing a door and receiving a blessing before the crew suited up and prepared to board the spaceship.
Maj Peake is employed by the European Space Agency (Esa).
Previous “Brits in space” have either been US citizens or had dual citizenship, or been on privately funded or sponsored trips.
At a press conference yesterday Maj Peake told how he was eagerly looking forward to seeing the Earth from space.
He said: “I don’t think anything can really prepare you for that moment.”
The crew will take six hours to rendezvous with the ISS, which passed directly over the launch site just before lift-off.
Prior to docking, they have to catch up with the space station, which travels at 17,500mph at an average altitude of 220 miles.
Sometimes a short rendezvous is not possible, and a crew has to revert to the longer flight plan. Shortly before 3pm, UK time, Russian mission control in Korolyov confirmed that Maj Peake’s team was conducting a short rendezvous.
Former army aviator and helicopter test pilot Maj Peake comes from Chichester in England while his wife is from Comrie in Perthshire.
His mission is called Prinicipia in homage to Sir Isaac Newton’s ground-breaking text on the physics of gravity and motion.