Operation Pitting will see the military also aid the evacuation of former British staff eligible for relocation under the Afghan Relocation and Assistance Policy (ARAP).
The operation will be commanded from the UK’s Permanent Joint Headquarters in Northwood, London.
It will be led by the 600 members of the Armed Forces who have already begun deploying to Afghanistan – with members of 16 Air Assault Brigade leaving this weekend.
Defence Secretary Ben Wallace said ensuring the safety of British Nationals is the UK's "top priority" and the military is "very well prepared" for the operation.
"Over the next few weeks, we shall all do our very best to support the Afghan government and those that have worked with us over 20 years," he said.
Watch: Afghanistan – What will the return of British troops to the country look like?
UK troops will also be providing force protection and logistical support for the relocation of British nationals where required and assist with the acceleration of the ARAP.
To accelerate the process, a small team of officials from the Home Office will assist the Foreign, Commonwealth & Development Office (FCDO) in Kabul, Afghanistan's capital.
They will be tasked with streamlining the processing of new visas and other documents needed for British nationals, former UK staff and other eligible people to leave Afghanistan and travel to the UK.
Home Secretary Priti Patel said the UK has a "moral obligation to support the fearless Afghan staff and their family members, who served alongside our brave troops in Afghanistan".
"No-one should have their lives put at risk for working with the UK Government, which is why we have significantly expanded and accelerated our dedicated resettlement scheme, deployed Home Office officials to help process British nationals for evacuation and waived visas for their dependants."
On 15 August, the Home Office said it had "resettled over 3,300 Afghan staff and their families who have worked for the UK".
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Cover image: British personnel deploying on Operation Pitting, the military's support for the evacuation of British nationals and former British staff from Afghanistan (Picture: MOD).