Ms Cafferkey, who first contracted the ebola virus in December 2014, gave birth to two healthy twin sons at a maternity unit within Greater Glasgow and Clyde on Tuesday 11 June.
“This shows that there is life after ebola and there is a future for those who have encountered this disease”
In a statement, she said her new sons showed that ”there is life after ebola”.
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,” she added.
Both mother and babies are doing well, noted the health board.
The Scottish nurse contracted the infectious disease while working in a hospital in Sierra Leone at the height of the outbreak. She flew back to Heathrow in December 2014 with a high temperature.
At the time, Public Health England staff, in charge of screening for the virus at the airport, took Ms Cafferkey’s temperature before allowing her to board a connecting flight to Glasgow.
But Ms Cafferkey subsequently became critically ill and had to return to London for life-saving treatment at the Royal Free Hospital in Hampstead.
After leaving hospital, Ms Cafferkey was told that she was under investigation by the Nursing and Midwifery Council, due to concerns from PHE.
However, in September 2016, she was found not guilty of professional misconduct in a fitness to practise hearing in which she was cleared.