The launch on an Ariane 5 rocket from Europe's spaceport in Kourou, French Guiana, came after a previous attempt on Thursday was called off due to the risk of lightning.
Despite cloudy skies, the rocket lifted off as planned at 09:14 am local time (1214 GMT) on Friday, as guests including Belgium's King Philippe watched from the Guiana Space Centre.
A little under half an hour later, the uncrewed six-tonne spacecraft separated from the rocket at an altitude of 1,500 kilometres (930 miles), which prompted an outbreak of applause at the centre.
After a few tense minutes, ground control then received the first signal from the spacecraft.
The sense of relief in the room was palpable.
"I was very stressed. That was a rollercoaster!" European Space Agency (ESA) director-general Josef Aschbacher told AFP.
"I'm extremely proud for Europe because JUICE is the biggest mission of the decade and the most complex ever sent to Jupiter," he added.
The spacecraft then successfully unfurled its array of solar panels, which cover a record 85 square metres (915 square feet).
It will need all the energy it can get when it nears Jupiter, where sunlight is 25 times weaker than on Earth.
- 'Off and running' -
"That's it. We're off and running," ESA's JUICE project scientist Olivier Witasse told AFP.
It will be another 17 days before the spacecraft deploys its antennae, and three months before a final performance review, said ESA's Nicolas Altobelli.
"Then we will begin the phase of interplanetary travel," he added.
The Jupiter Icy Moons Explorer (JUICE) will take a long and winding path to the gas giant, which is 628 million kilometres from Earth.
It will use several gravitational boosts along the way, first by doing a fly-by of Earth and the Moon, then by slingshotting around Venus in 2025 before swinging past Earth again in 2029.
When the probe finally enters Jupiter's orbit in July 2031, its 10 scientific instruments will analyse the Solar System's largest planet as well as its three icy moons -- Callisto, Europa and Ganymede.
The moons were first discovered by astronomer Galileo Galilei more than 400 years ago but were long ignored as potential candidates for hosting life.
However, the discovery of huge oceans of liquid water -- the main ingredient for life as we know it -- kilometres beneath their icy shells has made Ganymede and Europa prime candidates to potentially host life in our celestial backyard.
JUICE will turn its sights on Ganymede -- the Solar System's largest moon and the only one that has its own magnetic field, which protects it from radiation.
- 'Extraordinary mission' -
In 2034, JUICE will slide into Ganymede's orbit, the first time a spacecraft will have done so around a moon other than our own.
NASA's Europa Clipper mission, which is scheduled to launch in October 2024, will focus on Ganymede's sibling, Europa.
Neither mission will be able to directly detect the existence of alien life. They instead hope to establish whether the moons have the right conditions to harbour life.
Carole Larigauderie, JUICE project head at French space agency CNES, pointed out that a form of mucus had been found in a lake underneath a glacier in Antarctica, showing that life can survive in such extreme environments.
"If JUICE manages to prove that Ganymede is habitable so that we can go and find out in the future that there is life, that would be fabulous," she said.
The 1.6-billion-euro ($1.75-billion) mission will mark the first time Europe has sent a spacecraft into the outer Solar System, beyond Mars.
"This is an extraordinary mission that shows what Europe is capable of," said CNES head Philippe Baptiste.
Friday marked the second-last launch for the Ariane 5 rocket before it is replaced by the next-generation Ariane 6.
Repeated delays for the Ariane 6, as well as Russia pulling its Soyuz rockets in response to sanctions over the war in Ukraine, have left Europe struggling to find ways to launch its missions into space.
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