The babies – four girls and two boys – weighed between 1lb 7oz and 2lb 2oz and doctors confirmed they were not conceived through IVF.
Their condition in intensive care last night was described as “as good as could be expected”.
Yesterday’s successful Caesarean section birth – which involved 30 medical staff – was 14 weeks early.
It is believed to be the first case of sextuplets in Northern Ireland.
Neonatal consultant Dr Clifford Mayes said: “This is both a happy time and a potentially difficult time.
“This pregnancy isn’t the result of IVF. It is an extraordinary thing to have witnessed but you are also struck by the fact that there are little babies in intensive care.
“We have planned very carefully for today and today went as well as we had hoped it would.
“The care of the babies would be the care we would normally expect for any baby.”
The birth of sextuplets is rare, occurring in about one out of 4.5 million pregnancies.
Midwifery sister Patricia Denvir was the lead midwife involved in the operation.
“It is a very stressful situation both for our staff, all of the staff involved and also for the parents, but it’s a situation that went very well,” she said.
“The mother was very composed – under a very stressful situation, both parents were very composed and they dealt with it very well.
“It is a very emotional time but it’s also very stressful for all concerned.”
Dr Mayes said it would be impossible for a woman to go full term with six babies.
In December 2002, Rhonda and Noel Loughran, from Cabragh, Co Tyrone, became parents to only the 12th set of natural quintuplets to be born worldwide since records began.
The proportion of multiple births has increased by 20% in the last decade, figures for England and Wales show.
The most famous sextuplets in the UK are the Waltons, all girls, who were born in Liverpool in 1983.
Chief executive of the Twins and Multiple Births Association (TAMBA) Keith Reed said: “This is wonderful news.”
And while he said multiple births could present many difficulties for health professionals and parents, he said the experience can also be rewarding.
“Around half of the 11,000 multiple births each year are premature, resulting in one or more of their babies being cared for in a neonatal intensive care unit so our families understand the rollercoaster of emotions this family will be on,” he said.