It follows outcry over control of the new National Maternity Hospital
The new National Maternity Hospital will have no involvement from the Religious Sisters of Charity.
The order has announced it is to to give up ownership of the St Vincent's Healthcare Group (SVHG).
It comes after outcry over ownership of the hospital, which is to be built on a Dublin site owned by the healthcare group.
The Religious Sisters of Charity are majority stakeholders in that group.
In a statement, the healthcare group say: "The nature of the Sisters' involvement in their healthcare operations has altered significantly in recent decades, from predominantly unsalaried healthcare professionals to the situation today where they have no direct involvement in the provision of healthcare."
"Consequently, the Sisters have for many years been engaged in an on-going strategic review of their healthcare facilities, especially SVHG.
"This has involved finding the way forward that best perpetuates the vision and values of Mary Aikenhead, which are dignity, compassion, justice, quality and advocacy.
"That process has accelerated over the past two years and has also involved consideration of these issues by the Board of SVHG over the same period."
"The outcome of the process is that the Religious Sisters of Charity believe the future continued success of SVHG, and perpetuating the vision and values of Mary Aikenhead, can best be ensured by relinquishing their shareholding in SVHG".
Ownership of the group is to be transferred to a newly-formed company with charitable status to be called simply 'St Vincent's'.
The land the hospital is to be built on, which is currently subject to a rental agreement, is to be sold to SVHG at "commercial terms to be agreed, and the rental agreement will cease", it adds.
While the Religious Sisters of Charity say: "The Religious Sisters of Charity will end our involvement in St Vincent’s Healthcare Group and will not be involved in the ownership or management of the new National Maternity Hospital."
"Although the Sisters of Charity no longer have any direct involvement in the provision of healthcare services we remain dedicated to preserving the legacy of Mary Aikenhead, whose mission in life was to heal and care for the sick and poor.
"We believe that the future continued success of SVHG can best be ensured by our transferring ownership of the group to a newly formed company with charitable status to be called 'St Vincent’s'.
"The Religious Sisters of Charity will have no involvement in this new company."
The statement adds: "It is now time for us to relinquish completely our involvement in SVHG.
"We are confident that the board, management and staff of SVHG will continue to maintain a steadfast dedication to providing the best possible acute healthcare to patients and their families in line with the values espoused by Mary Aikenhead".
This proposal has the full support of the board of St Vincent's Healthcare Group.
Amnesty International has welcomed assurances by the congregation that medical ethics codes in St Vincent’s will be amended to ensure compliance with national and international best practice guidelines and Irish law.
"We welcome today's news that the Sisters of Charity will divest itself of ownership and management of the new facility.
"We had been concerned at the proposed involvement in women’s health services of a religious congregration whose ethos is inherently antithetical to women's sexual and reproductive rights.
"We also welcome the assurances given that the medical ethics codes of the new body to take charge of the national maternity hospital will align with best medical practice.
The Health Minister Simon Harris said: "The timing of this historic decision is very welcome.
"It directly addresses concerns regarding the question of religious influence in the new National Maternity Hospital and further illustrates the constructive role of the Sisters to facilitate this landmark project".
The Department of Health says it is continuing to engage with St Vincent's Healthcare Group and the National Maternity Hospital in relation to the project.
Minister Harris will update Government on the project next week.
In a statement, the National Maternity Hospital says it "warmly welcomes" the statement from The Sisters of Charity and the Board of SVHG.
"At all stages during the Kieran Mulvey mediation it was our clear understanding that the nuns never sought to exercise clinical control over the hospital and that the independent ethos of the new National Maternity Hospital would be preserved on relocation to the SVHG campus.
"We have worked closely with St Vincent's University Hospital for generations and we would like to acknowledge the outstanding contribution of the Sisters of Charity to Irish Healthcare over so many years.
"We would also like to acknowledge the support of the Minister, Simon Harris and the Department of Health and our own board and staff in being so steadfast during this process."
Former Master of the National Maternity Hospital, Dr Peter Boylan, had been a vocal critic of the involvement of the Sisters of Charity.
He stepped down from the board of the hospital as a result.
Speaking to Pat Kenny, Dr Boylan says: "I think the the work that they've done over the years in healthcare obviously has bee tremendous - clearly in the area of maternity care through it would have caused them enormous difficulties.
"I think so what they've done is the noble and correct thing to do".
Asked if he felt relieved and vindicated by this move, he said: "Yes and yes".
The announcement followed renewed pressure on Minister Harris to outline his progress on the new National Maternity Hospital.
On April 26th, he called for a "period of calm" to allow him to meet with the boards of both hospitals and pledged to provide an update by the end of May.
Social Democrats TD Roisin Shortall says while the announcement is a great start, caution is needed in relation to the new maternity hospital.
Speaking on Newstalk Drive, she argued: "From the point of view of the concerns that were expressed very loudly be taxpayers over recent weeks, I think a lot of those concerns remain.
"It's hard to understand what justification there would be for handing over a valuable public asset to private interests. This is a public hospital, publicly funded, to serve public patients - and I can't see any reason why it should not remain in public ownership," she suggested.
The Green Party, meanwhile, welcomed the announcement by the Sisters of Charity.
Green Party Deputy Leader Catherine Martin said: "This move will put an end to the row over the new National Maternity Hospital, with the religious ethos in SVHG being replaced by compliance with national and international best practice guidelines on medical ethics and the laws of the Republic of Ireland.
"This will ensure complete freedom from religious interference in the new National Maternity Hospital, and the wider SVHG.
"We need to press on with the development of the new NMH, as a priority. The women and children of Ireland deserve the best maternity care available – it’s time for the Government to deliver that now."