A judge overturned the decision taken by Basildon magistrates on Monday that Denise Giddings, 33, should be remanded in custody in London's Holloway prison.
She was charged with the abduction of baby Karli from the maternity unit of Basildon General Hospital in Essex a week ago.
In a statement read to open court after an hour-long hearing, Judge Philip Clegg said he had made his decision after reading psychiatric reports on Mrs Giddings.
"I am satisfied in this case that the public will not be in any danger by Mrs Giddings being out on bail. I have granted her bail on fairly stringent terms," he said.
"These terms will mean her residing at an undisclosed address and on a substantial surety."
Mrs Giddings, a mother of three from Lagndon Hills, Basildon, left court with her family for an unknown address. Barry Spanjar, her solicitor, said she was "relieved and a little bit tearful".
He refused to go into what was discussed in court, as the decision was made in chambers, with no members of the public or press present.
But he said: "Denise is very relieved and anxious to see her children. She wants to spend some time with her boys and have Christmas with her family."
Mrs Giddings' mother, father, sister and other members of her family were at court and she was expected to see them all yesterday.
Mr Spanjar said: "It is going to take time for her to find her feet again. She has had a horrendous last few days in Holloway prison and it will take some time to get back to some degree of normality." Mrs Giddings will appear again at magistrates court on Monday as part of normal procedure, when it is anticipated the case will be adjourned for six to eight weeks.
Karli was found after 14 hours and returned to her parents, Karl Hawthorne and his partner, Tanya, last Saturday. Mother and daughter were allowed home from hospital on Tuesday, travelling with a police escort.Reuse content