The 444 visa is a temporary visa that allows New Zealanders to visit, study, stay and work in Australia, as long as they remain a New Zealand citizen.
The changes were announced this afternoon, as part of a new government package to aide those affected by Covid-19 in Australia.
Morrison has pledged AU$130 billion over the next six months to help Australians who have found themselves out of work.
He said the AU$130 billion was to "support the jobs and livelihoods of the almost six million Australians who will need that lifeline in the months ahead".
The Australian government is also introducing a AU$1,500 "Job Keeper" payment, which New Zealanders on 444 visas will be eligible for.
Businesses will be paid up to AU$1,500 a fortnight, per employee, for the next six months.
The payment will be a flat rate of AU$1,500, regardless of how much they had previously been paid.
Earlier on Monday, Prime Minister Jacinda Ardern said she had spoken to Australia's PM Scott Morrison that morning and had again pushed the case for New Zealanders to be covered by any job scheme.
"It is a group I am concerned about. I have seen ongoing reporting of some of the issues that they're facing, and I see this as a unique situation. For me, this is a particular set of circumstances that I'm very keen to find a way to address."
Last week she had criticised the decision to leave New Zealanders out of some Covid-19 support packages, because New Zealanders do not get welfare benefits in Australia unless they have become citizens.
Australians do qualify for those benefits in New Zealand, and Australian workers here are also covered by the Covid-19 specific support measures.
Ardern has been highly critical of some of the Australian policies affecting New Zealanders, especially the policy of deporting those convicted of sentences totalling more than two years or on character grounds.
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"If anyone falls on a hard time, it's the same hard time," Morrison said.
"We're all in this together, that's what's fair, that's what's Australian."
Morrison said the Job Keeper payment was "to keep Australians in their jobs even when the work dries up".
According to Australian Treasurer Josh Frydenberg, the payments would also be available to part-time workers, sole traders and casuals who have been with their employer for 12 months or more.
Payments will flow from the first week of May but will be backdated to today. Employees stood down since March 1 will be eligible.
Ardern has responded to the news Kiwis are included in Australia's wage subsidy scheme, saying she had pleaded New Zealand's case several times, including on Monday morning.
"New Zealanders are a core part of the Australian workforce. Many are working on the front line in essential services. Others have built their careers there and paid taxes for years, so it's really pleasing the Australia Government has agreed to provide them a wage subsidy at their time of need.
"We need to unite and look after everyone to beat Covid-19 and Prime Minister Morrison and I are in regular contact about our respective efforts to beat the virus and support our people."
'The right thing to do is to look after people'
Wellington-born Alax Robinson has been living in Australia since 2017 and started an online petition, calling for Centrelink to support all Kiwis living there, late one night after losing his own job in a text message.
"I thought, 'what have I got to lose?'," Robinson told the Herald.
"I am trying really hard to channel all of my energy into something positive and this has been a really good thing for my mental health as well."
That petition has garnered more than 250,000 signatures of support.
Robinson said the Australian Government's announcement today was exciting and credited it as huge progress.
"It is really great that we are finally being acknowledged.
"Up until now none of the Australian politicians have really been talking about us, and so it has made a lot of people feel really abandoned.
"Especially people that have lived here for quite some time and have property here and pay taxes here."
The 35-year-old said he did not think it would have happened without Ardern going in to bat for them and without the petition on change.org.
"It is really exciting, however it is not perfect. Someone in my situation who started their job as a casual employee in October last year doesn't qualify for this.
"You have to have held that position since March 1, 2019."
It also presented a problem for small businesses who often did not have a lot of cash flow, he said.
"Many of them are operating on a month-to-month basis, just like most households do."
They were not going to be able to cover payments until they received back-dated pay in May, Robinson said.
The petition still asked the Australian Government to go further, he said.
"There is still a big gaping hole of people that need support that are not going to get it."
He said his message to Morrison was simple.
"The right thing to do is to look after people."
