Separated twins Hassan and Hussein Benhaffaf are expected to remain in hospital in Ireland for several days after returning home today.
Dubbed the "little fighters", the five-month-olds were brought back to Cork by the Irish Air Corps after medics at London's Great Ormond Street Hospital gave the all-clear.
Their parents Angie and Azzedine Benhaffaf appealed for privacy and said they would arrange a proper homecoming at a later date.
The couple, as well as experienced surgeons, have been taken aback by the speed of the boys' recovery just over six weeks since they endured a complex 14-hour operation.
They had been joined from the chest to the pelvis.
Health chiefs at Cork University Hospital (CUH) had been liaising closely with their counterparts in London ahead of the lunchtime transfer.
Deirdre Murray, consultant paediatrician at CUH, said: "We're delighted to hear that they have done very well following their surgery and we are looking forward to getting to know them.
"We also know that their parents are looking forward to spending some quiet time with them as a family after a difficult few months."
Dr Murray added: "We hope that they will only need to be with us for a couple of days, get back to being part of a normal family and just start treating them as separate little boys."
The Irish Air Corps said the family arrived in Cork Airport at 2.15pm after a smooth flight over the Irish Sea.
It is understood the twins will be monitored by CUH's paediatric team, headed by Professor Jonathan Hourihane, before a decision is made when they can be cared for at home in Carrigtwohill, east Cork.
Health chiefs said the family would appreciate privacy on their first day back.
Consultant surgeon Edward Kiely, who led a 20-strong team of medics to successfully separate the twins last month, made his last visit to them this morning.
The boys' hearts were not joined, but all of their other major organs, including their liver, gut and bladder, were and had to be separated. They have one leg each.
The surgeon gave the family the news they have been waiting for after checking the babies at 8.30am in Great Ormond Street and they were discharged two hours later.
The senior medic has said he was astonished at the speed of the boys' recovery and suggested it may be due to the twins' young age.
"Small children are as tough as nails and can cope with stresses and strains of operations that would be virtually impossible certainly at my age," he told RTE Radio.
"They shrug it off and they recover extremely quickly - whether you can describe that as fighting spirit I don't know but most children have it and I think it's as good a way of describing it."
The consultant, who is originally from Cork, also admitted growing attached to the twins.
"I think when you have children who are going to have something big done there is always a personal attachment," Mr Kiely said.
"They come from Cork and I'm from Cork so it's a bit more personal than many. In the end you do have some personal attachment, otherwise you just couldn't do the thing."
The Benhaffafs relocated their entire family, including daughters Malika, four, and two-year-old Iman, to London for the operation and recovery period.Reuse content