The council has said that the refugees will be resettled across two or three households in the district as part of the government's Afghan resettlement scheme following the takeover of Afghanistan by the Taliban.
Around 5,000 Afghan's will be resettled in the UK over the next year, with a total of 20,000 expected over the next five years.
The council have said that North Yorkshire is expected to become home to around 100 Afghan's who have been assessed as being "under serious threat to life" and are unlikely to ever return to their homeland.
The council have said that a private landlord has already offered a six-bedroom house as accommodation for refugees.
The project is being managed by Migration Yorkshire, North Yorkshire County Council and the Home Office and all costs are being funded by the Government.
Leader of Craven District Council, Cllr Richard Foster, said: "Craven is committed to doing its bit to resettle refugees from Afghanistan.
"We are very grateful to the private landlord who has made the effort to come forward and offer a property and I’m hopeful it will be used in the near future.
"Alongside a roof over their heads, resettling refugees requires us to consider a great deal more, including health and social care, integration into the community and education, so it will be important to work closely with North Yorkshire County Council and other district partners and agencies that have the expertise and resources to help."