Kiwis bringing their savings home must put them into a KiwiSaver fund.
The new rules are expected to kick in from 1 July next year.
Mr English said the scheme was an important economic step between the two countries.
"In particular, this will further help the free movement of labour between New Zealand and Australia and further strengthen our wider closer economic relations agreement," he said.
The transfer of retirement savings between the countries will also be exempt from entry and exit taxes.
Retirement savings transferred from Australia into a New Zealand KiwiSaver scheme can be withdrawn when members turn 60 providing they've retired, as set out under Australian scheme rules.
Under the Australian scheme, the money can be withdrawn when members reach 65, as per New Zealand KiwiSaver rules.
KiwiSaver members will not be able to withdraw money transferred from Australia to help them buy their first home, but can use the interest earned on those savings to do so.