“We welcomed 140 people on Monday and then around 50 daily are expected over the coming weeks,” said the regional prefect Fabienne Buccio.
French authorities said that families and individuals considered particularly vulnerable would be granted priority access to the new shelter.
Tents in the northeast of the sandy jungle have been removed to make space for the new shelter, about 125 converted containers.
Migrants will have to register to live inside the new camp and access toilets and showers.
“We want migrants to come here and rethink their entire journey with the help of organisations and authorities,” said Buccio.
“They need to understand that it is now impossible to reach the United Kingdom from here,” she added.
Although some still hope to reach Britain because of greater job opportunities and beacause they are more familiar with the English language.
“It’s like a prison here,” said Abdullah, a 25-year-old Iraqi. He and his friend Saad plan to stay in their tent despite freezing temperatures as they still want to reach Britain as soon as possible.
“Once you are in the new shelter, you won’t go to England anymore,” he added.
The jungle camp near the port of Calais hosts about 4,000 migrants since Sangatte was shut down in 2002 under British government pressure as it was encouraging illegal immigration to Britain.