Claims that British social services "forcibly removed" the baby girl from the woman's womb while she was on a work trip sparked a furore at the weekend.
But officials in Essex, east of London, said that health authorities had obtained a court order in August 2012 forcing the C-section "because of concerns about risks to mother and child".
A court judgment authorising the adoption of the little girl, named only as "P", revealed that the mother had bipolar disorder and suffered from "very intrusive paranoid delusions" when she failed to take her medication. She had spent several spells in psychiatric wards in Italy.
The mother, who came to Britain in 2012, was "profoundly unwell" and had been forcibly taken into psychiatric care a month before the birth, judge Roderick Newton said in his ruling in February.
He said the mother, who has two other daughters being cared for by their grandmother in Italy, was now in much better health and had sought to take the newborn home with her.
But he gave the go-ahead for the baby to be adopted in Britain, saying this was the best way to guarantee her a "permanent, predictable and stable home".
"If in later life P reads this judgment, as she may well do, I hope that she will appreciate that her mother in particular loved her and wished for her to return to live with her and to bring her up," Newton said.
The Sunday Telegraph newspaper reported that the mother, who cannot be named for legal reasons, is continuing to fight through the courts for custody of the child.
The Italian had come to Britain in 2012 for a two-week Ryanair training course when she was taken ill, the newspaper said.