The 84 detainees released so far will be monitored with ankle bracelets and mandatory curfews.
Under an agreement with the Coalition, they will also be barred from working with children and restricted in their movements around childcare centres and schools.
Breaching the rules will result in a five-year jail sentence.
Those released include a child sex offender and several murderers.
They were refused visas on character grounds but could not legally be deported, rendering them stateless.
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Home Affairs Minister Clare O’Neil has said the government would have preferred to maintain indefinite detention.
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“Some of those people have committed deplorable, disgusting crimes,” she said.
The government has said it had been preparing its response ahead of last week’s High Court ruling, but the opposition has criticised the delay.
Opposition leader Peter Dutton overnight blasted Prime Minister Anthony Albanese for travelling to the US for the APEC summit instead of fronting for the government.