The Albanese government on Monday announced 19,000 people who hold temporary protection visas or safe haven enterprise visas, can apply online for permanent visas from late March.
Only asylum seekers who entered Australia before Operation Sovereign Borders began in 2013 are eligible to apply.
Labor maintains a policy where people who arrived by boat after the operation came into place will never be resettled in Australia.
In a statement, the Asylum Seeker Resource Centre said it welcomed the end of a "cruel and rigged" process, but said 12,000 people were still waiting for a pathway to permanency.
"The significance of this announcement cannot be underestimated. We have tears of joy for all those who have been waiting for 10 years to have the permanency they deserve," resource centre advocacy director Jana Favero said.
Amnesty International Australia campaigner Zaki Haidari said the organisation was "relieved to see the happiness" the decision had brought for refugees, but was "pained" for the thousands left without a solution.
Government Services Minister Bill Shorten has refuted claims Labor's move will encourage people smugglers and result in more boat arrivals.
A cohort of people whose protection visas are due to expire soon will be invited by the department to have their applications fast-tracked.
The government has also set aside $9.4 million over two years to give the refugees free visa application help, through specialist legal service providers.
Immigration Minister Andrew Giles said Labor was putting an end to a decade of uncertainty for these refugees who worked, pay taxes and had built their lives in the Australian community.
"It makes no sense, economically or socially, to keep them in limbo," he said.
People who held temporary protection visas had to reapply every three years, with those holding safe haven enterprise visas needing to reapply every five years.
The more than 2500 people who were found not to be owed protection by Australia will not be eligible, and are expected to leave the country.
Home Affairs Minister Clare O'Neil warned asylum seekers the Australian Defence Force and Australian Border Force were patrolling the country's seas to intercept boat arrivals.
"Let me be crystal clear, if you try to enter Australia without a valid visa you will be turned back or returned to your port of origin," she said.
"There is zero-chance of settling in Australia under Operation Sovereign Borders."
For the more than 5000 people who are having their protection visa applications reviewed, this process will continue uninterrupted.
If an application for a temporary protection visa is sent back to the department by a court or tribunal, and the asylum seeker is found to be owed protection, they will be given permanent residency.
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