Some 7,000 migrants are thought to have settled in the camp in France which could be shut down in days.
Families were seen loading their belongings into suitcases and bags as they prepared to board coaches out of the camp.
The authorities are due to move in imminently to dismantle the camp before winter begins.
A Lille court has rejected a request from aid groups to postpone the closure, arguing that authorities are not ready to relocate its residents.
Charity groups warned that many of the migrants do not want to stay in France and may set up camp elsewhere to continue trying to cross the English Channel to Britain.
The French interior and housing ministers welcomed the court”s ruling and said the camp should be dismantled before winter sets in.
It comes after a female interpreter was raped at knifepoint near the Jungle, while two men held a blade to the throat of the journalist she was working with.
The pair, who were making a programme for the television channel France 5, were attacked by three men, who spoke Pashtun.
Migrants and refugees in the shanty town are being relocated around France or deported ahead of the closure.
Coach-loads of families are being bused out to start new lives elsewhere in France.
Young children were among those who boarded the coach on the camp”s fringe before it took them to new communities in the south of the country.
Among the first to claim a seat was Naqeebullah Noorzada, 44, from Afghanistan – who was with his three children aged eight, six and 10, and his sister-in-law.
He said: “There are a lot of problems here, particularly if you have children, so we are moving elsewhere in France, in the south near the Spanish border.
“We are at war in my country. We had to escape the Taliban. I want my children to have an education.
“We are happy to be moving out of here. We will be at peace. My first choice was London because I love the English and I speak good English.
“But wherever there is peace is my second choice.”
No date has been announced for the demolition of the camp but Calais Police Commissioner Patrick Visser-Bourdon visited the camp yesterday as eviction notices were served for shops on the site.