New Zealanders living in Australia for at least five years can apply if they earn the median wage or more, and pass security, character and health checks.
The "new pathway" means easier access to citizenship, which allows access to a range of welfare services.
The deal follows tensions over the deportation of New Zealand criminals under laws introduced last year.
These laws allow Australia to deport any foreigners sentenced to more than 12 months in jail.
Prime Minister Key previously said the issue was "undermining [a] special relationship".
"We traversed some of the concerns that we continue to have," he said in Sydney on Friday. "We appreciate the work that  [Australia has] been doing around ensuring that people can appeal those decisions."
Meanwhile, Mr Key formally extended the offer to take in some of the 267 asylum seekers awaiting deportation to Australia's offshore detention centre in Nauru.
"All I can simply say is the offer remains on the table," Mr Key said.
The Australian government is refusing to alter its border security policy, saying it is aimed at stopping the people smuggling trade.
The two leaders also said security agencies would increase cooperation and communication surrounding cybercrimes committed by "state and non-state actors".

The Australian hit a nine-under-par 63 at Sawgrass to move ahead of a group of five players that includes England's Justin Rose and Ireland's Shane Lowry.
Lowry picked up seven shots on the back nine to come home in a tournament record 29 strokes.
Masters champion Danny Willett is seven adrift on two under, while world number two Jordan Spieth is level par.
Rory McIlroy, the world number three, also finished nine shots off the lead after a 72 containing two birdies and two bogeys.
Day, starting on the back nine, began his round with three straight birdies and reached the turn in four under par.
He then added five more birdies when he got to the front nine to equal the course record shared by Martin Kaymer, Roberto Castro, Greg Norman and Fred Couples.
Lowry, 29, has recorded only one top-10 finish this season but joined Rose and American trio Bill Haas, Brendan Steele and Cameron Tringale in a homeward run that included chipping in for an eagle-three at the par-five 11th.
Willett and Spieth, both playing their first tournaments since an Augusta duel won by the Englishman, ended up well adrift on a day of low scoring.
Indeed, Spieth took a seven on the par-five ninth, his final hole, after taking five shots to get down from a greenside bunker.
The Australian government says up to 70,000 New Zealanders will be eligible for citizenship under a new agreement.
[NEXT_CONCEPT]
World number one Jason Day equalled the course record to take a two-shot first-round lead at the Players Championship.