The authorities say the evictions are needed to deal with an outbreak of scabies in the camps, where numbers have swelled in recent months.
The migrants have been trying to get to Britain, and say they have nowhere else to go after the camps are destroyed.
Police moved into the site after a deadline for people to leave expired.
Several busloads of police in riot gear arrived at the camps early on Wednesday.
After a stand-off with local activists, the officers moved in and told migrants to pack their bags.
Local officials say the migrants will be transported to new accommodation somewhere in the region, but initial attempts to persuade them to board buses were unsuccessful.
Most people at the camps believe the UK will be a more welcoming place if only they can get there.
The migrants have been sheltering under plastic bags and sheets, without water, power or even enough food.
The camps are a few hundred metres from a terminal where ferries take passengers and goods back and forth between France and the UK.
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