"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, $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.
Her comments come after more than 2,000 migrants were bused out of the Calais "Jungle" on Monday as French authorities began an operation to dismantle the notorious camp.
Rudd pledged to support the operation by bringing eligible children from France to Britain "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.