The former army pilot is making history as the first official UK astronaut.
Lift off occurred from the launch pad where, in 1961, Yuri Gagarin became the first human in space.
At blast-off, the rocket generated 422.5 tonnes of thrust – equivalent to 26 million horse power.
After one minute, the rocket was soaring upwards at 1,000mph (1,600km/h) and one minute later the four first-stage boosters strapped around the rocket fuselage were jettisoned.
Zero gravity was reached by the Soyuz spacecraft after nine minutes of travel.
Docking at the ISS is scheduled to take place at 17:24 GMT (23:24 local time).