From 1 January 2022, the PNG government will be given "full responsibility" for the 124 refugees and asylum seekers who remain there, she said.
The group will be given the option of permanent resettlement on PNG or they can be transferred to Nauru, with whom Australia last month signed a new memorandum of understanding to continue offshore processing.
Former Manus Island detainee Thanush Selvarasa was released from detention in Melbourne earlier this year.
He said his life and that of many other asylum seekers have been damaged irreparably by being held on PNG, and those who remain there need a "permanent solution".
"Day by day, we were destroyed physically and mentally. No one can live there anymore. It is hard to explain the island. It is a different type of torture," he told SBS News.
"We were punished for more than eight years. We are not a border protection tool."
Senator Nick McKim on Australia to end offshore processing of asylum seekers in PNG
Greens Senator Nick McKim said the past eight years of offshore detention have damaged Australia's humanitarian reputation internationally, with some nations such as the UK citing Australia as inspiration for their own immigration policies.
"There is no doubt that the men from Manus Island were - and in some cases still are - political prisoners," he said.
"They are like the corpses that used to be impaled on the walls of medieval cities to dissuade other desperate people from trying to enter."
Mr Rudd on Wednesday chastised the federal government for continuing the PNG deal over eight years, saying it was only ever supposed to last for one.
"Successive Liberal governments have ignored the provisions of the original policy on the proper standards of accommodation, health and other services to be provided to those being resettled," a spokesperson for the former prime minister told SBS News.
"From the moment it became clear that people weren’t being rapidly processed, they should have been brought to Australia for processing and then resettled in willing third countries like New Zealand.”
Refugee advocates have now renewed calls for Australia to pursue New Zealand's longstanding offer to resettle annually 150 refugees from its detention system.
David Burke, legal director at the Human Rights Law Centre, also said there were concerns about the ability of PNG to offer safe permanent resettlement for the remaining refugees.
"Shifting people from PNG to Nauru to continue to be warehoused on a remote island simply extends this cruelty," he said.
"We need an end to this cruel policy failure once and for all so people can finally start to rebuild their lives in safety.”
Labor's home affairs spokeswoman Kristina Keneally said offshore processing was "an important part of Operation Sovereign Borders", but the party supports the New Zealand resettlement offer.
In a statement, a spokesperson for the Department of Home Affairs said "regional processing arrangements in PNG and the management of individuals under those arrangements has always been the responsibility of the PNG government."
"PNG will continue to provide support to persons remaining in PNG until they either depart or are able to be independent and fully support themselves and their family," the spokesperson said. "Australia and New Zealand have a close and cooperative relationship and government officials regularly engage on a range of immigration, border and national security issues, including New Zealand’s generous resettlement offer."