Hughes said Moss was a dedicated public servant and leader who had made a number of significant improvements in what was one of the biggest and toughest roles in the public service.
During her tenure, fewer children and young people had entered care, social worker caseloads had been reduced, investment in iwi/Māori services had doubled and the agency had developed new whānau care partnerships with iwi and Māori organisations.
The commissioner said he respected Moss' decision to stand down.
"I commend Mrs Moss for doing what is, at this time, in the best interests of the agency.
"What she has done today is selfless."
The commissioner has appointed Sir Wira Gardiner as Acting Chief Executive.
Gardiner has whakapapa links to Ngāti Awa, Ngāti Pikiao, Te Whānau-ā-Apanui and Te Whakatōhea. He has been involved in significant interactions between the Crown and iwi on Treaty settlements and negotiating between parties on complex issues.
He was the founding director of the Waitangi Tribunal, head of the Iwi Transition Agency, and founding chief executive of Te Puni Kōkiri, the Ministry of Māori Development.
Davis, who is responsible for Oranga Tamariki, said Moss was stepping down from "one of the toughest roles in the public service" and he "respects the decision she has made and dignified way in which she has done it".
He said he welcomed Gardiner into the acting chief executive role.
"My focus is on working with the leadership of Oranga Tamariki, fixing the system and implementing the Government's work programme.
"Oranga Tamariki needs to be an enabler, a place whānau go to for help."
Crucial to this was partnership with Māori.
"Now we have a real opportunity to make that happen."
Davis said he was not Moss' employer, and she made the decision herself.
Asked if he thought she was the right person to be in charge, Davis said he didn't like to talk about chief executives he worked with.
"She has made the decision to step down, and I respect that decision."
Davis said he had met with Oranga Tamariki leadership before Christmas, and spelled out the direction he would like them to go in.
This would be more regionally-based, and not just partnerships with Māori but making Māori ways business as usual.
Before Christmas Davis refused to say he had confidence in Moss. Davis now said that was a "moot point".
"We were still developing a working relationship, now she has tendered her resignation that is a moot point."
Asked directly if he asked her to resign, Davis said he didn't.
"I am not her employer. No, I don't have that ability or power to ask a chief executive to resign."
Asked who the new chief executive should be, Davis said there were benefits "having someone familiar with the Māori world".
The Māori Party was calling for the next chief executive to be Māori. Davis said it would be the "best person for the job".
"It is probably one of the most difficult roles in the public service, we have to make sure we take our time to do it right and get the right person."
Davis could not specify a timeframe before a new chief executive was selected, saying it would take "as long as it takes".
"I wish [Moss] all the best. It is a very difficult role she has had over the last four years and I really wish her the best and respect her decision and the dignity in which she did it."
Moss has accepted a new role as the chief executive leading the Public Service's pay equity work.
Hughes said pay equity is one of the Government's priorities and Moss has the skills and experience to lead what is a significant body of work across the public sector.
"Mrs Moss led the successful pay equity claim for social workers at Oranga Tamariki- Ministry for Children and was also part of the team which developed and delivered pay equity to aged care workers. As such she has significant experience and expertise."
Moss will move into her new role on April 12. Her initial contract will run until March 31, 2022.
Her last day as chief executive of Oranga Tamariki will be February 28. Gardiner will join the agency on February 1 and begin his role as Acting Secretary for Children and chief executive of Oranga Tamariki on March 1.
A recruitment process will begin shortly to appoint a permanent chief executive.
The Maori Party Co-leader Debbie Ngarewa-Packer welcomed Moss' decision.
"This resignation is the result of the continued strong pressure of the Māori Party and our esteemed members, the Kahurangi [Dames]. We have forced Oranga Tamariki into acknowledging the institutional racism.
"Given that she has acknowledged the continued failings and systemic racism on her watch, Grainne Moss tendering her resignation was the only right thing to do.
"Our Māori Party policy, released during the election, is very clear – we must shut down Oranga Tamariki and start again with an independent mokopuna Māori agency.
"The Government must now implement that policy, and follow the advice of the Children's Commissioner – begin the process to disband Oranga Tamariki and shift the powers and responsibility to an independent by Māori, for Māori agency.
"As a first step to achieving that, Kelvin Davis must appoint a senior Māori leader as acting CEO whose one job is to dismantle Oranga Tamariki and ensure there is a smooth transition to the new regime."
The agency has been under intense scrutiny since video was published of the uplift of a week-old Māori baby in Hastings last year.
That event has led to no less than five reviews of Oranga Tamariki and its child uplift practices - an internal review, and inquiries by Whānau Ora, the Chief Ombudsman, the Children's Commissioner, and the Waitangi Tribunal.
The number of children in state care and the number of uplifts has fallen under Moss' watch, and partnerships are being created with iwi to prevent their tamariki from going into care or keeping them within extended family.
But many prominent Maori leaders remain deeply distrustful of Oranga Tamariki and felt that transformational change was yet to occur.