The 43-year-old from South Lanarkshire hailed their arrival, declaring that “there is life after Ebola”.
Ms Cafferkey contracted the virus in 2014 while doing aid work in Sierra Leone during the West African Ebola epidemic.
She spent almost a month in an isolation unit after being flown home.
The nurse survived the illness and was discharged from hospital but has been readmitted on a number of occasions.
Paying tribute to the NHS staff who have helped her, Ms Cafferkey said: “I would like to thank all the wonderful NHS staff who have helped me since I became ill in 2014 right through to having my babies this week.
“This shows that there is life after Ebola and there is a future for those who have encountered this disease.”
A spokeswoman for NHS Greater Glasgow and Clyde said both the mother and babies were “doing well”.
More than 11,000 people died as the disease took hold across the West African region between 2013 – when the outbreak was thought to have started in Guinea – and 2016, with a handful of cases treated in the UK.
And Africa is again in the grip of the deadly virus with the World Health Organisation poised to declare an international emergency over the Ebola epidemic in the Democratic Republic of Congo that has now spread to Uganda.
DR Congo’s epidemic is the second worst worldwide since the West African outbreak, with 2,084 cases and 1,405 deaths recorded since being declared last August.
The WHO said two people had died in Uganda after arriving with the disease from DR Congo.