Pen Farthing served in Helmand and set up the charity Nowzad to look after animals in Afghanistan.
The 'Pack Project' Facebook page said: "AMAZING news to start the week! The Nowzad rescue have confirmed today that they have received the 68 visas needed for their team to come to the UK!
"They have also received the permission for their dogs and cats to travel on the same flight!" They went on to give "A huge thank-you to Boris Johnson for approving" the travel.
They also went on to say: "There is still the issue of safe passage to the airport and the growing concern that Joe Biden and Kamala Harris still plan to pull out all troops on 31 August.
"This would leave thousands of vulnerable people without safe passage to safety as the airport will then be shut down."
Watch: Pen Farthing had refused to leave Afghanistan without his staff.
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Cover image: Former Royal Marine Paul 'Pen' Farthing.