The group says federal, state and territory parliaments should nominate a shortlist of candidates for head of state, which would then be put to a national ballot of voters.
The federal parliament would be able to nominate up to three people while states and territories would nominate one person each.
The ballot winner would get a five-year term and would be responsible for appointing a prime minister with majority support in the House of Representatives, or calling an election if that support does not exist.
But the head of state would have no authority in day-to-day governance or passing laws.
The model was developed across a two-year period, with more than 10,000 Australians consulted through surveys, polls and meetings.
ARM chair Peter FitzSimons said the 'Australian Choice' model brought responsibility to citizens to elect their own leaders.
"This will give all Australian voters a merit-based choice about who speaks for them as head of state," he said.
"The decision will be in their hands, unlike now, where it is luck of the draw who we get from the British Royal Family."
Movement research found 73 per cent of Australians would vote for a republic if the model was put to a referendum.
It also found 92 per cent of Australians are open to the idea of a republic, with just eight per cent opposed to any change.
Mr FitzSimons said having a specific model to allow for the change overcame the movement's main barrier.
"We've consulted, we've listened closely and Australians have told us this approach will give our nation the best chance of success at a referendum, with an overwhelming majority of Australians likely to back the change," he said.
Labor frontbenchers Mark Dreyfus and Matt Thistlethwaite congratulated the ARM on its model.
"The Australian head of state should be one of us: an Australian who lives with the Australian people," they said.
"Whilst constitutional recognition and a Voice to Parliament for First Nations people remain Labor's constitutional reform priority, it is important that all Australians have the opportunity to consider an Australian head of state in the future and the best model of appointment."
They said the nation needed its own head of state who reflected Australia's maturity, independence and unique identity.
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