On Twitter, Paul “Pen” Farthing shared a photo of Nowzad workers in the Pakistani capital of Islamabad, adding that they are in the custody of the British High Commission.
Its staff, who were hand-raising dozens of rescued animals, were unable to leave during the rushed mass evacuation from Kabul airport last month.
Since Mr Farthing returned to England at the end of August, he has been working to help evacuate 68 people, including Nowzad staff and their family members. Among them are 25 children and a newborn.
“It’s absolutely breathtaking. It still hasn’t really sunk, ”he said.
Mr Farthing’s campaign – known as Operation Ark – has sparked controversy, with the Defense Secretary saying it distracted attention from efforts to evacuate vulnerable people.
The former Royal Navy also apologized for leaving a curse-laden message for a government aide as he attempted to carry out the evacuation.
Foreign Minister Dominic Raab tweeted: “Glad the Afghan staff from Nowzad, who have been called in for an evacuation, made it across the border into Pakistan today. Our staff @ukinpakistan are helping them and we look forward to welcoming them to the UK in the coming days.
In other events, Saturday saw the Taliban hoist their flag above the Afghan presidential palace.
The low-key ceremony took place as the United States marked the 20th anniversary of the September 11 attacks.