Wafa Gul Akbarzai, who worked with British forces in Afghanistan, arrived in Yorkshire six weeks ago with his wife and four young children, as part of the Afghan Relocations and Assistance Policy.
The scheme was launched in April to help Afghans who have assisted the British military over the last 20 years and it was accelerated when US-led forces began to withdraw and the Taliban made rapid advances against government forces.
The insurgents have reclaimed control of Afghanistan after they took the capital Kabul on Sunday and thousands have been attempting to flee the country, as they fear persecution and violence.
Mr Akbarzai said: “I’m really feeling good and happy but very concerned about my country and future of my family.
“I am happy to be safe and thank the British government who have saved our lives, as we saved theirs in the battlefields. We really appreciate the British people and we will never forget they saved our lives.
"The British government has shown their commitment to their colleagues who worked with the British forces to ensure they were not left behind.”
Migration Yorkshire, which helps councils in Yorkshire take in refugees and asylum seekers, said hundreds are coming to the county through the Afghan Relocations and Assistance Policy.
So far 24 families, consisting of 174 people, have settled in Yorkshire and the Humber and another 10 are waiting to come to the region.
Dave Brown, head of Migration Yorkshire, said: “This region stands ready to support any humanitarian response to the situation in Afghanistan and to accept our fair share of people whose lives are at risk.
“We are proud of how Yorkshire and the Humber have supported Afghan families so far.”
People relocated in the UK are given permission to stay for up to five years initially and they can then apply for permission to stay permanently.
Accommodation and support are provided by councils, who receive funding from central government.
Around 900 armed forces are in Afghanistan helping to bring UK nationals home and secure the safety of selected Afghans.
Mr Raab said 150 British nationals were flown out on Sunday while 289 Afghan nationals were taken out last week. A further 350 British and Afghans will be taken out of the country in the next 24 hours.