Ardern said she knows some of the survivors and is proud to have played "even the smallest part" in the inquiry.
The duration of the Royal Commission has also been extended to four years to reflect the wider scope, Ardern said.
"Today paves the way for us to confront a dark chapter of our national history by acknowledging what happened to people in state care, and in the care of faith-based institutions, and to learn the lessons for the future," Ardern said.
She said of the 400 submissions received on the draft Terms of Reference, including faith-based institutions in the inquiry was one of the most strongly argued issues.
Cabinet confirmed the four other members of the Inquiry to serve with the chair Sir Anand Satyanand: Ali'imuamua Sandra Alofivae, MNZM; Dr Andrew Erueti; Paul Gibson; and Judge Coral Shaw.
The inquiry, announced by the Prime Minister and Martin in February, covers circumstances where the state directly ran institutions.
These include child welfare institutions, borstals or psychiatric hospitals, and where the Government contracted services out to other institutions.
The scope of the inquiry was wide, Ardern said. It covered a period of 50 years – from 1950 to the end of 1999.
Former Governor-General Sir Anand Satyanand is chairing the inquiry. He was with Ardern at the post-Cabinet press conference this afternoon.
It is a day for congratulations to the Government for its decision, Satyanand said.
"This Royal Commission is a huge undertaking; it will be the largest royal commission that the country has ever undertaken," Satyanand said.
Satyanand said the four other members of the Inquiry people with "very good pedigree to do the job."
"We are really well geared up to undertake this job efficiently and well," Satyanand said.
He said the $78 million price tag for the inquiry was "prudent."
"We are providing New Zealanders with a process of healing."
Ardern said it was "very hard to ignore" the strength of the submissions from the people asking for the scope to be expanded to include faith-based institutions.
Satyanand there is discretion to listen to accounts before 1950 and aftern 1999.
Ardern said the budget could increase, if the inquiry gets bigger.
Faith-based schools are also included in the inquiry.
Gloriavale could be included in the inquiry, Satyanand said.
Ardern said the Government has scrutinized the cost heavy – but that was the cost of having "thousands of voices being heard."
She said the Government has a "moral duty" here.
Ardern said if the Commission calls for it, the Government will issue a formal apology.
Asked if the Terms of Reference will look into compensation, Satyanand said that would be considered by the Royal Commission.
"Hearing the survivors' accounts is a principle task we have and that could come to us in a variety of fashions," Satyanand said.
"We must learn from the mistakes of the past, and take responsibility for them. That's why we have asked that the first interim report of the inquiry be focused on state care," Internal Affairs Minister Tracey Martin said.
That will be reported back by the end of 2020. A separate report will be focused on the abuse of children in faith-based institutions, she said.
Martin said the Government has not yet spoken to the churches about the decision.
"Unlike some similar overseas inquiries, the royal commission will take a broad view of abuse and consider physical, sexual and emotional abuse and neglect," Martin said.
Notably, the draft inquiry's terms of reference did not include churches.
In a letter to the Prime Minister in March, New Zealand Catholic Bishops Conference president Bishop Patrick Dunn called for a broadening of the inquiry's terms of reference.
"We are of the view that when the commission's work turns to the institutions themselves, included among them should be a range of church institutions. In this way we too will be active contributors and learners within the Royal Commission of Inquiry."
The Anglican Church's top general synod committee also sent a formal letter to Ardern and Martin urging the Government to broaden the terms of reference to include church-related bodies.
At the time, Ardern said while what churches have to say could feed into the inquiry, she stood by her belief that the inquiry should look primarily into what happened to children while in the care of the state.
Satyanand said he had received more than 400 submissions from the public. He submitted his findings and a report with new suggested terms of reference to cabinet in May.
Timeline:
February, 2017: The Human Rights Commission published an open letter in the Herald, calling for a comprehensive inquiry and public apology to those who were abused.
July, 2017: Then-Opposition Leader Jacinda Ardern wrote to Prime Minister Bill English urging him to instigate an inquiry.
August, 2017: UN recommends NZ Government hold an independent inquiry into historic state abuse.
November, 2017: The Government includes the setting up of an inquiry into the abuse of children in state care as part of its 100-day plan.
February 1, 2018: Prime Minister Jacinda Ardern officially announces a Royal Commission of Inquiry into Historical Abuse in State Care.
March 30, 2018: The Royal Commission of Inquiry invites submissions from the public on the draft terms of reference for the inquiry.
April 30, 2018: Submissions for the draft terms of reference for the inquiry close.
May 30, 2018: Royal commission chair Sir Anand Satyanand files his report with Internal Affairs Minister Tracey Martin.
November 12, 2018: Prime Minister Jacinda Ardern expands the scope of the inquiry to include churches.
