The two boys - who fled trouble in their own countries - are being cared for by Tom and Lucy Etum-Ejon, of Chapeltown.
The couple hope their experience will help inspire more people to consider foster care during Foster Care Fortnight, which runs from Monday May 11 to Sunday 24.
Mr Etum-Ejon, 54, is a full-time foster carer, and his wife Lucy, works in a care home.
One of the boys is from Eritrea and has been with the couple for 18-months.
With Mr and Mrs Etu-Ejon's help, he has now been granted asylum in the UK.
The second 16-year-old they are fostering is from Albania and is currently seeking asylum in the UK.
Mr Etum-Ejon, said: “For me, the most rewarding thing about fostering is noticing the relationship that develops between us.
"If you show someone love, and they respond to that in a positive way, there’s no better experience.
"Both boys have improved their English so much since they came to stay with us.
"I’m so proud of them both, they’ve gained a lot of confidence and I hope to be able to continue to see that grow."
Mr and Mrs Etum-Ejon were born in Uganda but have lived in the UK for over 25 years.
They both worked with the Centre of English Studies Leeds for more than ten years, offering home stays to foreign students for a period of a few weeks up to a year.
After hearing an advert on local radio, they decided to look into fostering with independent fostering provider and social enterprise, Five Rivers Child Care, which has an office in Doncaster.
Mr Etum-Ejon, said: “Having moved to a different country ourselves, we know how it feels to have to leave your home to live somewhere new.
" We can understand how strange everything can feel which helps us empathise with how they might be feeling.”
Both boys initially came to the couple on a short-term stay, but have agreed that if they’re able to, they’d both like to stay with the couple until they are 18.
A report shared earlier in the year showed that there are a record 78,150 children in care and in Yorkshire and Humberside alone another 910 foster carers are needed to meet demand and help provide a safe home to vulnerable children and young adults.
Stephanie Todd, team manager for the Doncaster office in the Yorkshire area at Five Rivers Child Care said: "They’re such an inspirational example of a couple who are able to offer a loving home for young people in need. It’s fairly unusual for us to be able to find a long-term caring home for young people seeking asylum.
"Tom and Lucy have not just provided these two boys with somewhere to stay, but they’re helping them seek asylum in the UK, which they may struggle to do alone.
“The Coronavirus pandemic hasn’t stopped us recruiting foster carers, as the need for children and young people to have stable and caring foster carers has not diminished, and in some areas we have seen the need increase."
For more information on foster care contact Five Rivers Child Care on 0345 266 0272 or visit www.five-rivers.org.