Opponents say they believe St James's Hospital in Dublin "is the wrong site" for the new facility
The acting Health Minister Leo Vardakar says the debate is over in relation to the new National Children's Hospital.
Children, parents and health professionals are among those welcoming the news that the facility has got the go ahead.
The hospital will be going to tender in the coming weeks, and is expected to open in autumn 2020 - at a projected cost of €650m.
An Bord Pleanála granted permission for the new facility in Dublin city, with the hospital approved as designed.
Eilísh Hardiman, CEO of the Children’s Hospital Group, welcomed the news.
She told Newstalk Breakfast earlier that construction on the new hospital will begin in the summer, with construction set to take four years.
John Pollock is director of the National Paediatric Hospital Development Board.
He says the granting of planning permission for the new children's hospital is great news, which will allow for a world class facility.
While acting Minister Varadkar told Newstalk Lunchtime he hopes those opposed to the location will come onboard.
However, opponents to the central Dublin location have said the new hospital would be better located on a campus off the M50 motorway - with many suggesting the campus of Connolly Hospital in Blanchardstown as a more appropriate site.
The proposed location in Dublin city has raised concerns over potential problems accessing the hospital during busy periods for traffic.
Children's Rights campaigner Aisling McNiffe is opposed to the location for a number of reasons.
Dr Finn Breathnach, spokesperson for Connolly for Kids Hospital, spoke to the Pat Kenny Show about his disappointment with the latest development, saying "we believe it is the wrong site".
Some 3,700 people will be employed at the hospital when it opens, with another 2,300 positions set to be generated during construction.
It has been previously suggested that the new hospital could end up costing more than €700m - over €50m more than originally estimated. However, the Children's Hospital Group says the cost is likely to remain at €650m.
13-year-old Ashleigh Kiernan, who was treated for cancer aged 7 in Crumlin Children’s Hospital, says the new facilities are going to be great for sick kids.