Ms Cafferkey, 43, fell ill with the disease after carrying out volunteering work in Sierra Leone, where the disease killed as many as 4,000 people during an outbreak in 2014.
The news of the arrival of the twin sons was broken by the boys' father, theatre director Robert Softley Gale, on social media.
The Daily Record reported that Mr Gale had written on Facebook: “Hello world. Meet these two amazing boys. Born at 10.05 and 10.08 this morning – 5lb 14oz and 5lb 8oz. Mum and boys doing brilliantly. Names to follow.”
Ms Cafferkey later told the paper: “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 Greater Glasgow and Clyde health board told the BBC: "We are pleased to confirm, on behalf of Pauline Cafferkey and her partner, that she gave birth on Tuesday to healthy twin boys at a maternity unit within Greater Glasgow.
"Both mother and babies are doing well."
Ms Cafferkey had spoken of her joy at beating the virus previously, telling the Scotland on Sunday in 2015 that she was 'happy to be alive'.