Paul “Pen” Farthing set up the Nowzad shelter in Afghanistan’s capital city in the mid-2000s after serving in the British forces.
His campaign to get himself, his staff, and his animals to the UK – dubbed “Operation Ark” – after the Taliban took over Afghanistan has caused some controversy in recent days.
Although visas were granted for his 24 staff and their dependents, Mr Farthing refused to leave without the animals – of which there are up to 200 in total.
On Friday, the Ministry of Defence (MoD) announced that Mr Farthing, the cats, and the dogs have been taken into Hamid Karzai International Airport with the help of armed troops.
But it is not known whether any of the Nowzad shelter staff will be also leaving Afghanistan.
In a tweet, the MoD said: “Pen Farthing and his pets were assisted through the system at Kabul airport by the UK Armed Forces. They are currently being supported while he awaits transportation.”
It added: “On the direction of the Defence Secretary, clearance for their charter flight has been sponsored by the UK Government.”
On Thursday, Mr Farthing said that his group was “turned away” from the airport due to paperwork changes made some hours earlier by the US.
He said that his group was then caught up in the chaos following a suicide bombing outside the airport building – that the so-called Islamic State claimed responsibility for – in which more than 180 people have died.
Mr Farthing said on Twitter: “Went through hell to get there & we were turned away into the chaos of those devastating explosions.”
Before the MoD announced that Mr Farthing and his animals were set to fly out, Defence Secretary Ben Wallace said his staff had faced abuse from Mr Farthing’s online supporters who accused the MoD of “blocking” their flight out of Kabul.
Mr Wallace complained that the “bullying, falsehoods and threatening behaviour” towards MoD staff were distracting from the focus on evacuating the most vulnerable people.
Speaking to LBC, he said: “I think it has taken up too much time of my senior commanders dealing with this issue when they should be focused on dealing with the humanitarian crisis.”
Mr Wallace also said that Britain’s evacuation effort in Kabul has entered its final hours and has largely ended processing new evacuees, and that the Baron Hotel processing centre has now been closed.