More than 150 mothers and babies were transferred to the new Cork University Maternity Hospital from the three existing facilities in the city over the weekend.
Management said yesterday that the move to the new site on Saturday had passed without incident.
The new state-of-the-art facility in Wilton is now open to admissions, following the amalgamation of units at three Cork hospitals: St Finbarr's, Bons Secours and Erinville.
The first baby born at the new facility was Kacper Poslada Ciolek, who was delivered by his mother Luiza at 10.20pm on Saturday night. He weighed 3.030kg, with Luiza and his father Maciej having travelled from Kenmare for the birth.
Kacper's parents are originally from Poland.
Newly appointed director of midwifery, Geraldine Keohane, said five babies were born there late on Saturday.
Consultant obstetrician/gynaecologist Prof John Higgins said yesterday the new mothers had been very impressed with the appearance of the hospital and the facilities on offer.
"The feedback so far has been great. They have been part of the excitement and the mothers themselves have been thrilled.
"We intend to bring together the very best of traditions from three maternity hospitals here to Cork University Maternity Hospital," Prof Higgins added.
"There really isn't a more special moment than the birth of new life and, whatever the hour, mothers and babies in Cork know that their midwife will be there for them."
Among the first arrivals was Caitriona Hawkins, the mother of twins Peter and Brian, who were born last Tuesday at St Finbarr's Hospital in Cork city.
Their father, Richard Hawkins from Ballygarvan, Co Cork, said: "It is very bright and very modern. We are pleased to be here. We have a two-year-old boy Timmy as well who we had at Finbarr's. St Finbarr's was very good too but we are happy to be here."
Irish Nurses Organisation midwives voted on Friday night to transfer to the new hospital following agreement with the Health Service Executive on the immediate provision of additional qualified midwifery and nursing staff.
Key elements included 20 additional midwifery and nursing staff, who will start immediately.
Also included is the confirmed recruitment of 82 additional midwives and the immediate filling of three midwife skills facilitator posts, who will orientate all of the new staff.