The announcement, from a regional official, came with fires still burning in the camp, after blazes were set overnight and in the morning.
The camp has become a key symbol of Europe’s migration crisis, with its residents desperate to reach the UK.
Authorities have been bussing migrants to shelters around France since Monday.
Fabienne Buccio, the prefect of Pas-de-Calais, said: “It’s the end of the Jungle, our mission is over. There are no more migrants in the camp.”
Five thousand people had been sent to departure points from where they would be taken to reception and orientation centres around the country, she said. By the evening, she added, 1,500 minors would be sent to reception centres. These centres would then stop receiving more people to make sure no more minors arrived in Calais. The camp had an estimated 6,000-8,000 residents. The BBC’s Simon Jones, who is at the camp, says it is possible a large number have disappeared – either to squat or sleep rough around Calais or go to other towns of their own accord. The authorities fear they will return to set up camp again once the clearance is over.
More than 1,200 police officers have been deployed for the clearance operation in Calais.