The annual domestic fees for a Bachelor of Arts at Melbourne's Monash University total about $7765.
Avondale College, one of the country's largest schools, has already received an inquiry from an Australian family, interested in how they can qualify their children for free study here.
Education Minister Chris Hipkins confirmed Australians can get free study and training if they have lived here for at least three years.
"Any Australians wanting to take up fees-free tertiary study will need to meet the three-year residence requirement that currently applies to accessing interest free student loans and student allowances. This will also apply to other residents from different countries," Hipkins said.
"Australians who have been ordinarily resident in New Zealand for less than three years will continue to pay domestic fees."
Currently Australians pay domestic student tertiary fees but cannot access student loans or support unless they live here for at least three years.
National's tertiary spokesman Paul Goldsmith said the three-year minimum requirement is not new.
"There is precedent for it in the sense that the access to interest-free student loans and allowances have that three-year stand-down.
"But you would have to change the arrangement. At the moment it is quite clear - for the purposes of fees, [Australians] are treated as domestic students. It is a change to the agreement."
Goldsmith said he didn't think Australians would expect to get free study here, however it was a change to the current policy of treating Australians as domestic students, "and that has to be managed".
National's education spokeswoman Nikki Kaye said the free tertiary policy was being rushed, and there were potential unintended consequences, including for schools.
"When we have principals saying they have had calls from Australia...we may see Australians taking advantage of the policy, and we may see more Australian kids in our schools."
New Zealand expats currently in Australia could return or send students and their siblings to stay with relatives while studying, Kaye said.
"I'm not saying that is all bad... but the point is about what we need to do to plan for particular policies like this," Kaye said. "Schools need time to plan."
Hipkins dismissed the idea people could cross the Tasman as a result of the new scheme.
"It may prove an added attraction to Australians already considering moving to New Zealand, but by itself it is hard to imagine it would motivate Australians to shift here for the three years needed to access fees-free study.
"I am taking advice on the likely impact on student numbers but over-all I expect it will increase participation over time - even if some students consider delaying their study while the fees-free policy is phased in."
New Zealanders or eligible Australians who have not studied at tertiary level before will be entitled to one year of free tertiary study or post-school training from next year. The policy will be extended to two years free in 2021, and three years free in 2024 - or more rapidly, if conditions permit.
After a meeting with Australian Prime Minister Malcolm Turnbull in Sydney earlier this month, Ardern indicated Australians wanting to access the fees-free scheme would need to have lived in New Zealand for a certain length of time.
She also reiterated her position to hike fees for Australian students, if Kiwis are charged international fees in Australia.
A measure in the Australian budget would see Kiwis treated as international full-fee paying students, although many would be able to access student loans for the first time. That measure is currently stalled in the senate and is unlikely to be implemented in the foreseeable future.
Another sore point in the trans-Tasman relationship has been the Barnaby Joyce affair. In August, Australian Foreign Minister Julie Bishop said in August she could not trust a future Labour Government if it had colluded with Australia's Labor Party to uncover the fact then deputy prime minister Joyce was a New Zealand citizen.
Bishop's comments came after news Hipkins had asked parliamentary questions about citizenship after a chat with a staffer for the Australian Labor Party. He has denied knowing there were questions about Joyce's citizenship, saying he asked the questions of Dunne to clear up the law.
The government expects 80,000 people will use the new policy. The plan is going to cost $380,000.
