Legislation introduced to the Senate on Monday would temporarily allow the asylum seekers to live freely in Australia until they are resettled by a third country.
The offer of evacuation would only be made to people who have not had adverse security assessments made against them by the nation's intelligence agency ASIO.
People evacuated to Australia would also be provided with access to medical treatment.
Greens immigration spokesman Nick McKim said the legislation did not require the government to permanently settle people in Australia, but instead offered a compassionate and practical solution until a deal had been clinched with a third country.
"It was the ALP (Labor Party) which sent every one of these people to Manus Island and Nauru in 2013, which means that Labor has a moral responsibility to end their exile," he said.
"Offshore detention has been a humanitarian calamity, and one of the darkest and bloodiest chapters in our country's story - it is time we wrote the ending, and this bill will help us to do that."
Senator McKim said the legislation was a critical step in ensuring asylum seekers "finally get the dignity and respect they deserve, and the chance to rebuild their lives in safety and freedom".
Australia maintains a policy of never allowing asylum seekers to resettle in the nation if they arrive by boat.
Kurdish-Iranian refugee and journalist Behrouz Boochani, who was detained on Manus Island but now lives in New Zealand, will visit Parliament House in Canberra on Tuesday in support of the evacuation push.
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