The royal commission will look at the causes of systemic problems and the failure of officials to identify and correct them, and report back next March.
It follows media reports that revealed the serious abuse of children detained at the Don Dale Youth Detention Centre outside Darwin.
After holding his first Cabinet meeting since the election, Prime Minister Malcolm Turnbull says the issues raised highlight the overrepresentation of Indigenous youth in detention.
"It's important to note that the matters of concern at the Don Dale Centre are in relation to the treatment of all youth in detention centres. It's also important to recognise, in the Territory, a significant number of these young people are Aboriginal and Indigenous people. Indigenous Australians make up 45 per cent of the 10- to-17-year-old population of the Northern Territory but 95 per cent of that age cohort in detention."
Territory Chief Minister Adam Giles has told the ABC the disturbing images seen on the network's Four Corners program highlight the need for significant reform.
He has rejected calls for his State Government to step down and has welcomed the appointment of former Territory Supreme Court justice Brian Ross Martin to lead the inquiry.
"He's a person who comes with a range of experience from across Australia in many jurisdictions, but also within the Northern Territory, as having been the former Chief Magistrate of the Supreme Court between 2004 and 2010. So he does have a lot of historical context for the Territory."
Justice Martin has told a media conference there is much to be done.
"Whether racism does or doesn't play a role will form part of the inquiry. This is about child-protection systems, it's about the culture. You'll notice that the terms of reference include questions about the culture within the system. And, naturally, if people believe that racism plays a role, then that's going to be the subject of evidence before the commission."
Federal Attorney-General George Brandis says the Commissioner has also been asked to determine whether there have been any violations of the law.
"To consider whether any such treatment might have been a breach of any Commonwealth or Northern Territory law, a breach of the Northern Territory's duty of care or other relevant duty, a breach of human-rights obligations adopted by Australia or the Northern Territory, or a breach of any relevant policy, rule, procedure, standard or management practice applicable to those facilities."
Labor frontbencher Ed Husic has told Sky News he thinks it is appalling it could happen in Australia because he believes the country operates on a higher standard than much of the world.
"When I watched that program on Monday night, what struck me was that there had been work done to investigate and these abuses had been brought to light and the reports had been kept secret -- which is bad on two fronts. One is, obviously, that the people that were responsible for such mismanagement and poor treatment were not held accountable. And, two, that there's no effort through the process of transparency to make sure that things are set right." Greens leader Richard Di Natale told Sky News it should be followed by a national inquiry into Indigenous incarceration.
"Now you do it in stages. Stage one should be to look at those urgent issues within the Northern Territory, to provide a set of recommendations and to ensure those recommendations are adopted. The last thing we want is the situation we saw with (the Royal Commission into) Aboriginal Deaths in Custody, where a number of recommendations aren't even adopted. We know what needs to happen. So, a commitment to adopt those recommendations in full. Address the Northern Territory issues first, deal with that, and then move on to a broad-ranging national inquiry." Meanwhile, the Northern Territory government is looking for alternative locations to hold nearly 40 children detained at the Don Dale Centre.
