The baby girl was delivered by a policewoman after passersby alerted officers that the 35-year-old Romanian woman had gone into labour, Il Messaggero reported.
The child, named Irene and weighing 2.9 kilograms, was born at around 2am on Piazza Pio XII, a small square off St Peter's Square.
The newborn and her mother, Maria Claudia, were then taken to the nearby Santo Spirito hospital, where they were paid a visit by the papal almoner, Archbishop Konrad Krajewski.
Krajewski, who was appointed almoner – a centuries-old role that involves helping the poor and needy – in November 2013, offered the woman and her daughter a year's free accommodation at a nun's residence in the city's Primavelle district.
Vatican spokesman Father Federico said Krajewski visited the woman because he knew her, while adding that he repeatedly offered her shelter but she refused.
Maria Claudia went to the square with her partner, a 40-year-old also from Romania, and other homeless people looking for shelter from the cold when she went into labour.
Many of Rome's homeless sleep under the colonnades of St Peter's Square each night.