The Health Information and Quality Authority is to investigate the circumstances surrounding the care and treatment provided to Savita Halappanavar.
Ms Halappanavar died on 28 October in University Hospital Galway following a miscarriage.
HIQA said it made its decision after considering information from the hospital and the HSE "to ascertain the facts about the tragic case".
Its investigation will assess whether the services provided complied with the National Standards for Safer Better Healthcare and national and international evidence of what is known to achieve best outcomes.
The terms of reference and membership of the HIQA investigation team will be published when finalised.
A clinical review by the Health Service Executive is also being carried out into the death which is expected to be completed by Christmas.
Tony O'Brien, Chief Executive designate of the HSE welcomed the fact that HIQA has decided to accept its invitation to set up a statutory inquiry into Mrs Halappanavar's death.
Mr O'Brien said that he believed the HIQA inquiry would add to public confidence overall.
He said that the HSE is obliged to carry out its clinical review into Ms Halappanavar's death, but said that he felt obliged to ask HIQA "to add to that process."
Tánaiste Eamon Gilmore welcomed the HIQA investigation, saying that while he wouldn't rule out a public inquiry, the danger is they "very often spend a long time being mired in legal argument."
"What is needed in this case is to get an inquiry that gets to the bottom of what happened, establishes the facts, established the truth," he said.
Minister meets Savita's husband
Minister for Health James Reilly has had a private meeting in Galway with Praveen Halappanavar and his solicitor Gerard O'Donnell.
Mr Reilly expressed his condolences to Mr Halappanavar on the death of his wife and said he would reflect on the concerns of the family.
Mr O'Donnell said the meeting was appreciated, but he set out clearly his client's position from the start: the request for a full, sworn public inquiry remains.
The solicitor went on to say that the Government could appoint a High Court judge to oversee a swift inquiry and establish the truth of what happened to Savita.
Otherwise, he said, he and his client would forge ahead, and if their requirements are not met they would consider making an application to the European Court of Human Rights.
Asked about the possibility of exploring a commission of investigation, Mr O'Donnell said that too, like the HIQA inquiry, may not go far enough.
Quinn says legislation is needed
Meanwhile, Minister for Education Ruairi Quinn has indicated that legislation will be needed to deal with Ireland's position on abortion.
He said anyone looking at the 1861 laws on abortion would consider legislation the most appropriate way forward.
Speaking at Dublin Castle this morning, Mr Quinn said that he would be bringing his views to Cabinet next week.
He refused to say whether he believed there should be a public inquiry into the death.
The minister also said the comments made by President Michael D Higgins earlier this week were appropriate.
Separately, the expert group has made a number of recommendations on how the Government could provide legal clarity on the issue of abortion.
A section of the group's report, seen by RTÉ's Prime Time, contains a number of possibilities for the Government on clearing up the legal grey area.
It suggests introducing guidelines as a speedy solution, or bringing forward legislation, either with or without regulations.
The full report goes to Cabinet next week.
Clinical review has to reassure women
Minister Reilly has said the HSE's clinical review into the death will go ahead because it has to reassure women using Galway hospital that it is safe.
Speaking in Galway, he said the review is moving ahead apace and the information gathered can be supplied to HIQA.
He said a HIQA inquiry would add another dimension to this.
"HIQA have form in this area in being utterly independent and doing extensive investigations that often uncover a lot more than the core issue.
"The obviously core issue here is how the tragic death of Savita Halappanavar occurred and is there anything that could have been done to prevent it."
Asked whether a compromise could be reached so that Mr Halappanavar's wishes for a public inquiry could be accommodated, he said the investigation has to be completed first.
Depending on what the investigation throws up, he said further actions may be necessary at that point in time.
"So I've ruled out nothing... we must get to the truth of what happened to assure ourselves that we have a safe service for all our citizens."