Congenital heart disease is the most common birth defect in Northern Ireland, with around 250 babies born with the condition every year, according to the Children's Heartbeat Trust charity.
But, a consultation was launched after the Royal Belfast Hospital for Sick Children's service was deemed unsustainable due to the numbers of patients it deals with - around 90 per year.
The board recommended developing a children's cardiology centre in Belfast.
John Compton, the Chief Executive of the Health and Social Care Board, said: "Our job is to assess a population and say how best should we provide services to that population?
"In this context, it is much better, I believe, to build a service round an all Ireland solution. Rather than leave a service which has uncertainty and which has fragility - that I think is irresponsible," he added.
In a statement, the Department of Health confirmed that a working group's preferred option was for surgery and interventional cardiology to be carried out in Dublin.
Children and parents will travel to Our Lady's Children's Hospital, Crumlin, while work gets underway on building a new super hospital.
Enhanced transport links will be put in place and surgeons from Northern Ireland will work alongside clinicians in Dublin. Belfast will receive new investment in cardiology facilities, including MRI.
The working group included clinicians, parents of children with congenital cardiac disease, parents' group representatives, service providers and commissioners.
Following the recommendation on Thursday, Health Minister Edwin Poots said he wanted to hold further discussions with representatives in the Republic before he makes his final decision on the matter.
My key priority in all of this is to ensure the delivery of a safe and sustainable service for these vulnerable children in so doing, I want to ensure that we have fully explored every possibility for addressing the concerns which have been raised with me by parents and by consultants.
Health Minister Edwin Poots
The Minister added: "No-one should underestimate the sensitivity and scale of the task undertaken by the Working Group. I recognise that at times it has been a challenging and difficult process for all involved especially the families.
"I want to thank everyone who played a part for their energy, honesty and dedication. It is important that we recognise and thank, not just the Working Group, but all the mothers, fathers, grandparents and family members who came forward on behalf their own children to public meetings, focus groups or to speak to me directly."
Back in February, UTV revealed that the Belfast Trust was in favour of moving some children's cardiac surgery to Dublin.
According to a documents obtained by patients' families under the Freedom of Information Act, the Trust favours a gradual transition taking no longer than a year.
The document said: "The resulting combined all-Ireland surgical service would have a case load of at least 650 surgical patients per year, easily meeting the minimum number of 400 paediatric surgical procedures per annum."
The Children's Heartbeat Trust has been campaigning to keep services at the Royal open.
Its chairman, retired paediatric cardiologist Dr Connor Mullholland, said the Trust's conclusion is "ill-informed and ill-advised" and that children's lives may potentially be put at risk.
He said: "It does not, at this point, support the evidence from several reviews of the cardiac surgery within the Children's Hospital."
Parents are also claiming the move to Dublin will put their children's health in danger.
Joanne Clifford said that if the services had been in the Republic when her baby was diagnosed with a heart problem, she would not have been able to travel with her child due to receiving an emergency caesarean.
"It's frightening, the whole thought of it," she added.
Ms Clifford said that the minister needs to listen to the clinicians and staff in caring for the children at the Royal Hospital.
"The clinicians deal with the kids day in, day out. They know the children, they know the emergencies as well."
Teresa Moss's daughter Riley had open heart surgery just over a week ago at the Royal.
She said the Board's decision has left her "devastated."
"To hear that decision just broke our hearts.
"The services here have saved Riley's life at least three times," she said, adding that the care the infant is receiving in Belfast is exceptional.
Ulster Unionist Health spokesperson, Roy Beggs MLA said that the Health Minister has not clearly explained why the service is unsustainable.
"The final decision lies with Edwin Poots. He can say no to this recommendation," Mr Beggs said.
"This is not a time for the Minister to be shirking his responsibilities to the Northern Ireland public who depend on the Health Service, for which he is solely accountable."
Maeve Hully, Chief Executive of the Patient and Client Council, said that it was important to continue monitoring the situation.
"I think this has been a difficult process for everybody who has been involved in trying to make sure that clinicians, families, the voluntary organisations have all been heard in the process.
"So coming to the final option is something that is representative of what people have been saying around the working group table."
She added that going forward, the Patient and Client Council would make sure that what parents are telling them is heard by those comissioning health services.