The climbdown by the Prison Service follows a legal challenge by the 24-year-old woman, who claimed that the decision to deny her a place in the unit at Holloway prison, north London, was unfair and unlawful.
She will now be allowed to care for her baby in either Styal prison, in Cheshire, or New Hall, in West Yorkshire.
The move to overturn the original decision has infuriated staff at Holloway, who had argued that the woman was a risk to other mothers and babies in the unit because of her unpredictable and violent behaviour.
The woman, a former psychology student, had been sentenced to five years' custody for slashing the face of a female friend with a craft knife in an argument over a man.
A board of professionals, including prison governors, psychologists, health visitors, social services and probation staff and a midwife, decided the woman was unfit to have a place in the 17-place Holloway mother and baby unit. The decision followed allegations of attacks on two other women in the pregnant women's unit.
The woman, who claims she was victimised by some other prisoners for being well-spoken and anti-drugs, denies both attacks. She admits to helping herself to a carton of milk to which she was not entitled.
The woman, who did not realise she was pregnant until she was jailed, gave birth to a baby girl at the Whittington hospital, north London, earlier this month.
For the past week, the pair have been in a private ward at a top London hospital, while the legal wrangle is being resolved. The woman, who has a National Health Service bed, is under the guard of two prison officers.
Earlier this week, midway through a hearing at the Court of Appeal, the Prison Service agreed to set up a new board to reconsider the woman's case.
The reconstituted board, which is chaired by Linda Jones, the Prison Service's director of women, will meet the woman and her barrister at Prison Service headquarters this morning and will suggest that she is moved to a mother and baby unit at another prison.
Harry Fletcher, of the National Association of Probation Officers, said: "This is totally unprecedented. If this decision has been taken without any new evidence it undermines the judgement of prison professionals." He said the Prison Service would need to create single units for mothers who were regarded as a possible risk to others.
Staff morale at Holloway has plummeted and the governor, Mike Sheldrick, who took the original decision to deny the woman a place, has been off work due to illness for two weeks.Reuse content