Britain pledges millions to secure Calais border
"Whilst responsibility for Calais lies with the French government, the juxtaposed controls are a vital part of the UK's border security and are a valuable economic link," Rudd told parliament.
"That's why the UK government will be contributing up to £36 million (40 million euros, $44 million) to maintain the security of these controls, to support the camp clearance and to ensure in the long-term that the camp is kept closed."
The home secretary said the funding would also be used to "help keep children safe in France" but stressed that it was not offered "unconditionally".
"We will continue to work with the French government to ensure that the clearance operation is full and lasting," she said, adding that French authorities faced a "huge challenge" in clearing the camp.
The pledge came after more than 2,000 migrants were forced out of the Calais "Jungle" on Monday as French authorities began an operation to dismantle the notorious refugee camp.
The clearance operation is expected to last three days after which the sprawling shantytown - one of the biggest in Europe - will be razed.
The settlement situated on wasteland next to Calais port, where migrants have established camps for over a decade, has become a symbol of Europe's failure to resolve the worst migration crisis in its post-war history.
Aid agencies have warned that some migrants could try resist being relocated and more than 1,200 police officers are being deployed to prevent any unrest.
Police fired tear gas to disperse migrants at various points around the camp on Sunday night.
Rudd pledged to support the operation by bringing eligible children from France toB ritain "as quickly and as safely as possible" in the coming days and weeks, without specifying numbers.
Almost 200 children have already been transferred to Britain from Calais, including 60 girls, many of them at "high risk of sexual exploitation," Rudd said.
The dire security and humanitarian situation in the Jungle has been a bone of contention between France and the UK for years.
The centre-right front-runner in next year's French presidential election, Alain Juppe, has called for the UK's border with France, which was extended to Calais under a 2003 accord, to be moved back to British soil.