It is the second successful delivery of conjoined twins at the hospital in two years. The girls were delivered by Caesarean section and are doing well, medical chiefs said.
It is not yet known whether surgeons will carry out an operation to separate the girls.
In September 1995, Chloe and Nicole Astbury were born at St Mary's - the first Siamese twins in Britain for 10 years. They were joined from the breastbone to the navel and shared a liver but died just over a month later.
About 60 per cent of Siamese twins, which occur about once in 100,000 births, are stillborn.
The mother was under the care of St Mary's hospital's top team of consultants, which was involved in delivering the Astbury twins in 1995.
Dr Mike Maresh, 47, clinical director of obstetrics. He has been involved in delivering all 10 sets of Siamese twins born at St Mary's in the last decade.
Dr Maresh was assisted by consultant paediatric surgeon Alan Dickson. Both consultants continued to keep a close watch on the mother and would be monitoring the twins' progress in the weeks to come, a hospital spokesman said.
The twins' parents, who have not been named, come from south Manchester and are believed to have no other children. The days-old baby girls are said to share a liver.
A spokesman for Central Manchester Healthcare Trust said the family had requested that they be allowed privacy and did not want interviews. A spokesman said the twins both had all limbs intact. The babies were not on ventilators and were generally "doing well".
Dr Maresh said that the twins had a "good chance" of survival: "They're very healthy."Reuse content