Former swimwear model Miss Mills, 35, who lost a leg in a car crash, has steel plates fitted in her hips which make natural childbirth impossible.
Macca's nephew Josh McCartney said his father Mike had called and told him about the new addition to the family.
A source at the hospital added: "Paul has been at her bedside all day. Heather is resting."
Sir Paul and Heather married in June 2002 in a fairytale wedding at a Scottish castle, they announced they were expecting their first child in May this year.
The ex-Beatle already has three children - James, 25, Mary, 33, and fashion designer Stella, 31, - by first wife Linda, who died in 1998.
He also has step daughter Heather, 39, from Linda's first marriage.
