Over one-third of France's "Jungle" camp's population left for 80 reception centres across France on Monday.
At least 2,318 migrants left the squalid conditions of the camp in Calais as France begins the process of dismantling it.
The demolition crew will start tearing the camp today and is expected to complete by Wednesday evening, French officials told AFP.
"Tonight, 2,318 migrants have been housed. 1,918 adults left Calais, boarding 45 buses heading towards 80 welcome centres located in 11 of France's regions. And 400 minors have been directed towards and also housed at the temporary centre, where they will wait for their cases to be studied, joining the 200 minors already there. There are therefore 600 isolated minors who are safe within the temporary reception centre (CAP). The first step has been taken today, it was done calmly and under control and we must of course continue," Reuters quoted French interior minister Bernard Cazeneuve as saying.
The migrants were asked to move or face deportation if they decided to stay in France, AFP reported.
French authorities said those who agree to be relocated can apply for asylum in France. Those who don't, however, can face deportation.
On Sunday, flyers were distributed telling migrants in text and pictures to show up at a hangar near the camp. The migrants began arriving early on Monday at meeting points set by the French authorities as part of a full evacuation and demolition of the camp, according to an AFP journalist at the scene.
Some 6,000 to 8,000 migrants will be moved to reception centres across the country. The move allows the closure of the camp which was home to over 7,000 refugees mostly from Afghanistan, Sudan and Eritrea in the past 18 months. The camp has strained relations between France and Britain and caused tensions with locals in Calais.
Jean-Marc Puissesseau, chief executive of Calais port where migrants in January briefly occupied a ferry, told BBC radio he was "a very, very happy man."
"It's for us really the D-Day," he said, hailing an end to the "constant stress" of drivers fearful of being ambushed by migrants, AFP reported.
Wahid, a 23-year-old Afghan expressed relief that he was being sent to a place "better" than the Jungle. "We don't know yet where we are going, but it will obviously be better than the Jungle, which was made for animals not humans."
However, amid relief over getting residency in France, some migrants vowed not to go to the shelter to which they are designated. They still hold on to the dream of going to England.
"They'll have to force us to leave. We want to go to Britain," Karhazi, an Afghan told AFP.
"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.
The first group of children with no ties to Britain arrived in the UK from the French "Jungle" migrant camp in Calais on Sunday. Britain began taking in children who had a family connection in the UK last week. Under a new legal Dubs amendment, a limited number of vulnerable child refugees are allowed entry into Britain even if they do not have family already living in the country.