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.
QSjJbCXlou8Image source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…