All but one of the 43 Papuans who landed on Cape York in January have been granted three year temporary protection visas, which allow the asylum seekers access to Centrelink (welfare services), medicare (medical services) and trauma counseling.
The final man remains on Christmas Island while his case is considered.
Their spokesman, Herman Wainggai, 32, said he had fled persecution.
"Me and my friends we come to Australia because we are under pressure from the military government of Indonesia," he told an impromptu news conference.
"In West Papua land (there is) no free(dom) to talk about our human rights."
Mr Wainggai choked back tears as he spoke about seeing his friends shot by Indonesian security forces.
"West Papua people wish for freedom," he said.
"West Papua people wishes for peaceful way to solving the problem in West Papua."
Mr Wainggai said he had been jailed twice for raising the Morning Star flag in Papua and he feared he would be "disappeared" if he was jailed again for his political activities.
The group will settle in Melbourne with help from the Red Cross and the Victorian Foundation for survivors of Torture.
Welcome protection
The lead lawyer accompanying the group, David Manne, from the
Refugee and Immigration Legal Centre in Melbourne welcomed the decision to grant the group protection visas.
“These decisions recognise the West Papua refugees' clear and compelling need for protection from brutal human rights abuses which have occurred on a daily basis over a long period at the hands of the Indonesian authorities," he said.
Mr Manne confirmed the group had several unaccompanied children and said young children were often targeted by Indonesian authorities, though he did not give examples.
Still no ambassador
The decision to grant protect to the West Papuans has caused tension in Australia’s relationship with Indonesia, with Jakarta withdrawing its ambassador to Australia, Mohammad Hamzah Thayeb, over the incident.
Australia’s Foreign Affairs Minister Alexander Downer says there is still no indication of when the ambassador will return.
Nationalist anger in Indonesia is running high over the decision, with critics accusing Canberra of secretly plotting the breakaway from Jakarta of the separatist province and likening it to the 1999 independence crisis in East Timor.
Mr Downer has told ABC Radio National that there was still no word on when the ambassador might return.
"That's entirely a matter for Jakarta, it's not going to be helpful for me to speculate," he told ABC Radio National.
"We weren't altogether surprised at their reaction and we understand that there are strong feelings about this issue in
Indonesia.”
"I think it's better that we just wait until the dust settles before getting into too much commentary on it," he added.
“Difficult” relationship
Indonesia’s President Susilo Bambang Yudhoyono said relations with Australia had entered a “difficult phase” and that he would now review cooperation aimed at curbing people smugglers who use Indonesia as a stop off point to Australia's north.
"Ties between Indonesia and Australia are now entering a difficult phase that is full of challenges," President Yudhoyono told a news conference in Jakarta.
Indonesia has repeatedly asked Australia to send the group back and has vehemently denied allegations that they would be targeted by Indonesia's military.