The 'Britain's Got Talent' judge missed auditions for the show on Monday and was rushed into hospital.
She safely gave birth to little girl Hollie Rose Hughes but has been in a critical condition for the past three days. She is now stable.
Spokeswoman for Amanda and husband Chris Hughes said this evening: "Hollie Rose Hughes was born on 23 January 2012.
"She is healthy and weighed in at 6.1lbs but Amanda has been in a critical condition for the past three days."
"She is now stable and we expect her to make a full recovery very soon. We thank you for respecting their privacy at this time."
The 40-year-old already has a six-year-old a daughter Lexi.
She had suffered a miscarriage back in 2010 and endured the heartache of a stillbirth last March, when she was due to have a boy.