The rocket departed from the European Space Agency's (ESA) launch centre in Kourou, French Guiana, on the northeast coast of South America at 4.17am (0717 GMT) on Tuesday on the first stage of a seven-billion-km, 10-year journey to reach the comet 67P/Churyumov-Gerasimenko.
Two launch attempts last week were cancelled due to bad weather and technical problems.
The Ariane-5 rocket lit up the partly cloudy equatorial night sky and was visible from the ground for more than a minute.
It is scheduled to fly for more than two hours before its upper stage re-ignites and then releases the Rosetta spacecraft.
"This mission will attempt to see material that dates from the formation of the solar system," said Phillipe Kletzkine, ESA's lead scientist for Rosetta's comet-landing probe.
"Comets are small masses far from the sun in a sort of deep freezer. For four-and-a-half billion years they have been kept in deep freeze. The importance of this mission to identify and analyse this material, as it was during the formation of our planet and at the beginning of life," Kletzkine said.
"Comets are small masses far from the sun in a sort of deep freezer"
Scientists believe comets may contain chemical and physical records from the time the solar system was formed about 4.6bn years ago.
The Rosetta mission will attempt to discover the secrets of how life began on Earth - and perhaps even elsewhere in the universe.