A group of Sudanese and Eritrean migrants, mostly men, queued in the early morning darkness outside a hangar where the camp's 6,000-8,000 occupants will be sorted into groups and put on buses for shelters across France.
A first coachload carrying 50 Sudanese left at about 8:45 am (0645 GMT), heading for the Burgundy region of east central France.
The clearance operation is expected to last three days after which the sprawling shantytown -- one of the biggest in Europe -- will be razed.
"I feel very happy, I've had enough of the Jungle," said 25-year-old Abbas from Sudan, who was bundled up in a woolly hat and coat against the cold.
"There are a lot of people who don't want to leave. There might be problems later. That's why I came out first," he added.
The settlement situated on wasteland next to Calais port, where migrants have established camps for over a decade, has become a symbol of Europe's failure to resolve the worst migration crisis in its post-war history.
Aid agencies have warned that some migrants could try resist being relocated and more than 1,200 police officers are being deployed to prevent any unrest.
Police fired tear gas to disperse migrants at various points around the camp on Sunday night.
Riots erupted when French authorities razed the southern half of the settlement in March.
Bashir, 25, also from Sudan, began queueing at 4:00 am (0200 GMT), four hours before the hangar serving as a bus station opened.
"Anywhere in France would be better than the Jungle", he said with a smile.
Giving up on Britain
The closure of the camp is aimed at relieving tensions in the Calais area, where clashes between police and migrants trying to climb onto trucks heading to Britain are an almost nightly occurrence.
Hours before the evacuation began some migrants were still clinging to hopes of a new life across the Channel.
"They'll have to force us to leave. We want to go to Britain," said Karhazi, a young Afghan, among many of the migrants with contacts in Britain.
A Syrian man named Sam who spent 13 months in the Jungle told AFP he had fled the camp at the weekend to another site about 12 kilometres (seven miles) away where he said "dozens" of migrants were hiding out to avoid being moved.
French authorities have said those who agree to be moved can apply for asylum in France.
"We have yet to convince some people to accept accommodation and give up their dream of Britain. That's the hardest part," Didier Leschi, head of the French immigration office OFII, told AFP.
Flyers distributed by French officials on Sunday instructed the migrants in Arabic, Tigrinya, Pashto and other languages to gather from 8:00 am.
They will be separated into four groups for families, single men, unaccompanied minors and other people considered vulnerable before boarding one of 60 buses which will take them to nearly 300 shelters nationwide.
British officials have been racing to process child refugees seeking to be transferred to Britain before they become scattered throughout France.
By Saturday, the number of minors given a one-way ticket to Britain under a fast-track process for children launched a week ago stood at 194, according to France Terre d'Asile, a charity helping in the process.
Most have relatives across the Channel but 53 girls without family in Britain also left France at the weekend.
A spokesman for Britain's interior ministry confirmed it had begun taking in children "without close family links" in the country.
Adult migrants with relatives in Britain have complained about being left out in the cold. Some have vowed to keep trying to stow away on a truck or to jump onto a train entering the Channel Tunnel.
Dozens of migrants have died in such attempts.
The dire security and humanitarian situation in the Jungle has been a bone of contention between France and Britain for years.
The centre-right front-runner in next year's French presidential election, Alain Juppe, has called for Britain's border with France, which was extended to Calais under a 2003 accord, to be moved back to British soil.