Following sporadic outbreaks of unrest overnight, the migrants chose instead with calm resignation to be relocated in France while their asylum requests are considered.
By lunchtime more than 700 had left the squalid shanty-town outside Calais on France's northern coast for reception centers across the country. Hundreds more queued outside a hangar, waiting to be processed before the bulldozers move in.
French officials celebrated the peaceful start to yet another attempt to dismantle the camp, which has become a symbol of Europe's failure to respond to the migration crisis as member states squabble over who should take in those fleeing war and poverty.
But some aid workers warned that the trouble overnight, when some migrants burned toilet blocks and threw stones at riot police in protest at the camp's closure, indicated tensions could escalate.
"I hope this works out. I'm alone and I just have to study," said Amadou Diallo from the West African nation of Guinea. "It doesn't matter where I end up, I don't really care."
The Socialist government says it is closing the camp, home to 6,500 migrants, on humanitarian grounds. It plans to relocate them to 450 centers across France.
Many of the migrants are from countries such as Afghanistan, Syria and Eritrea and had wanted to reach Britain, which is connected to France by a rail tunnel and visible from Calais on a clear day. Some had wished to join up with relatives already there and most had planned to seek work, believing that jobs are more plentiful than in France.
Britain, however, bars most of them on the basis of European Union rules requiring them to seek asylum in the first member states they set foot in.
Even as the process began, the fate of about 1,300 unaccompanied child migrants remained uncertain.
French Interior Minister Bernard Cazeneuve urged Britain last week to step up efforts to identify and resettle child migrants. London has given priority to children with family ties and discussions are underway with Paris over who should take in minors with no connections.
Britain's Home Office said on Monday it had reluctantly agreed to suspend the transfer of more children, on the request of the French authorities.
For now, children will be moved to converted shipping containers at a site on the edge of the Jungle before they are interviewed by French and British immigration officials, a spokesman for the U.N. refugee agency in Geneva said.
"It's cold here," said one Sudanese teenager who identified himself as Abdallah. "Maybe we'll be able to leave in a bus later, or next week, for Britain."
Armed police earlier fanned out across the Jungle as the operation got underway.
Interior Ministry spokesman Pierre-Henry Brandet said that authorities had not needed to use force and that the large police presence at the camp on Monday was just for security.
RAZING THE CAMP
Aid workers went from tent to tent, urging migrants to leave the camp before heavy machinery is rolled in to start the demolition.
The hundreds who volunteered on Monday to move on were each given two destinations to chose from before being bussed to the reception centers. There they will receive medical checks and if they have not already done so, decide whether to apply for asylum.
The far-right National Front party said the government plan would create mini-Calais camps across France.
Officials expect 60 buses to leave the camp on Monday and the government predicts the evacuation will take at least a week.
Many tents and makeshift structures that had housed cafes, bakeries and kiosks lay abandoned. On the side of one wooden shack a message to British Prime Minister Theresa May had been scrawled in spray-paint: "UK government! Nobody is illegal!"
Despite the calm, charity workers expect hundreds will try to stay and cautioned that the mood could change later in the week when work begins on razing the camp.
"There's a risk that tensions increase in the week because at some point the bulldozers are going to have to come in," said Fabrice Durieux from the charity Salam.
Others warned that many migrants who remained determined to reach Britain would simply scatter into the surrounding countryside, only to regroup in Calais at a later date.
"Each time they dismantle part of the camp it's the same thing. You're going to see them go into hiding and then come back. The battles will continue," said Christian Salome, president of non-profit group Auberge des Migrants.