The 40-year-old actress was rushed to hospital on Monday in labour with her daughter Hollie Rose. She is now stable, but is expected to take a while to recover.
Her husband has told of his gratitude to medical staff who brought the Britain's Got Talent judge back from the brink.
Chris Hughes, married to Amanda since 2008, has been with her since she was admitted to hospital on Monday morning and is indebted to the medical team.
A spokeswoman for the couple said: "Chris would like to thank all the medical staff and everyone who has been involved in Amanda's care."
Her little girl, who weighed in at just over 6lbs, is said to be healthy.
The TV favourite, who was due to be on the BGT panel at auditions this week, already has a daughter, Lexi.
But complications during that pregnancy with a low lying placenta meant she gave birth by Caesarean section.
The couple's spokeswoman said: "Until Amanda is in a position to indicate what she wants to say, there's no more information I can give."
She is thought to have needed transfusions after losing a lot of blood. Bleeding is one of the most common complications during childbirth.
Experts said this can be caused by tearing, the placenta becoming trapped inside, or because the uterus has not contracted after the birth.
But doctors emphasised that after transfusions women usually get better quickly with no long-term effects.