The controversial policy saw many refugees being sent to remote islands in the Pacific for processing, where they did not have access to the Australian legal system.
The newly-installed Labor government has said it also hopes to quickly resolve the case of 80 Sri Lankans being held on Nauru.
Evans said the seven Myanmar nationals, who arrived in Australia in August last year, will be brought back from Nauru and settled in Brisbane by the end of the year.
"There's no reason why they shouldn't be processed quickly," Evans told local radio on Monday.
"In fact in my view they should have been processed some time ago, but we're keen to resolve their issues."
John Howard, the former prime minister, introduced the refugee policy in 2001 following a surge in the number of illegal immigrants heading for Australian shores.
David Manne, a spokesman for the Refugee and Immigration Legal Centre who had been representing the Myanmar refugees, said the men were delighted to hear the news about their asylum.
|A surge in the number of illegal immigrants led |
Howard to introduce the policy in 2001 [EPA]
"They were very happy, extremely relieved about the news and really looking forward to being able to rebuild their lives and to make a real contribution in the future in Australia."
On Sunday a team of immigration and intelligence officials flew to Nauru to expedite the processing of the Sri Lankans still being detained there.
Evans also denied that dumping the 'Pacific Solution' policy meant the new Labor government of Prime Minister Kevin Rudd was softening its stance on border security.
"There's no suggestion of us weakening the policy in terms of border security and intercepting boats," he said.
Evans said a $438m detention centre set up between Australia and Indonesia on remote Christmas Island would remain in operation.
The new government is also expected to scrap a refugee swap deal made between Howard's government and the US in April, where Cubans held in Guantanamo Bay were to have been resettled in Australia and refugees from the Nauru camp settled in the US.
Although the deal was agreed, no refugees were ever swapped under the programme.