One of the boys was hooded and cuffed to a mechanical restraint chair wearing a "spit hood".
The Northern Territory`s Attorney General John Elferink has been stripped of his corrections portfolio.
The report raised questions about an institutionalised culture of abuse at corrections centres in the Northern Territory, an administrative district that covers a large part of Australia`s north.
`Shocked and appalled`
Prime Minister Malcolm Turnbull said the treatment of youths by the Northern Territory corrections system needed a thorough inquiry.
"Like all Australians, I have been deeply shocked, shocked and appalled, by the images of mistreatment at the Don Dale centre," Mr Turnbull said.
"We will be establishing a royal commission into these events, into this centre; we intend to do so jointly with the Northern Territory government.
"We will get to the bottom of what happened here ... we want to know why there were inquiries into this centre which did not turn up the evidence and the information that we saw on Four Corners last night."
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