Asylum-seekers who try to reach Australia by boat are either turned back or sent to remote camps in Nauru and on Papua New Guinea's Manus Island.
Refugee advocates and medical professionals have long criticised conditions in the camps, where some detainees have been held for years.
The secrecy provisions were introduced in 2015, making it a jailable offence for immigration department workers to speak out about conditions in the centres.
He told parliament last week the 2015 changes had "not kept pace with the developments in the modern border environment".
"The definition of the information to be protected has been refined to include only certain kinds of information" such as national security and defence, Dutton added.
The previous provisions were set to be challenged in the High Court by rights group Doctors for Refugees, which welcomed the government's U-turn.
"This is a stunning victory for anyone in Australia who believes people who are concerned about abuse or neglect should be allowed to speak out," Barri Phatarfod from Doctors for Refugees said in a statement Monday.
The detainees will be moved to third countries such as the US and Cambodia or be resettled in PNG.
Canberra has been criticised for its asylum-seeker policies but defends its tough stance as necessary to stamp out people-smuggling and stop asylum-seekers dying at sea in rickety boats.
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