A spokeswoman for the couple made a statement on behalf of the record producer, PA reports.
© Rex Features / McPix Ltd/Rex Features
"Chris would like to thank all the medical staff and everyone who has been involved in Amanda's care," she said.
"Until Amanda is in a position to indicate what she wants to say, there's no more information I can give."
Holden's condition was changed from critical to stable yesterday and she is being treated in an intensive care unit. She is expected to make a full recovery.
It was reported earlier today that Holden and her newborn daughter Hollie Rose Hughes were "fighting for life" after the birth.
> Amanda Holden: 'I might make Simon Cowell godfather to baby daughter'
Watch Michael McIntyre and David Walliams congratulate Amanda Holden on the birth of her baby below:
