The process of dying in an assisted suicide after an initial approach to a doctor in Victoria state takes at least 10 days, so the first patient could die from swallowing a lethal cocktail of chemicals on June 29.
Strict rules are designed to prevent terminally ill patients from travelling from overseas or interstate to access the laws.
Health minister Jenny Mikakos said she expected as few as one patient a month would be helped to die in the first year.
"We anticipate that once the scheme has been in place for some time, we'll see between 100 and 150 patients access this scheme every year," Ms Mikakos told the Australian Broadcasting Corp.
"In the first year, we do expect the number to be quite modest - maybe only as low as a dozen people," she added.
Four Victorian Roman Catholic bishops have signed an open letter describing the move as a "new and troubling chapter of health care in Victoria".
The letter said: "We cannot co-operate with the facilitation of suicide, even when it seems motivated by empathy or kindness."
Any health practitioner can conscientiously object to taking part in the euthanasia process.
The euthanasia system has been implemented over 18 months since the state parliament passed the laws in 2017.
Australia's sparsely populated Northern Territory in 1995 became the first jurisdiction in the world to legalise doctor-assisted suicide for terminally ill patients. But the Australian parliament overturned that law in 1997 after four people had been helped to die.
The Australian parliament does not have the same power to repeal the laws of states such as Victoria, which is home to one in four Australians.
The parliament of Australia's most populous state, New South Wales, rejected a doctor-assisted suicide bill by a single vote two weeks before the Victorian law was passed.
Queensland and Western Australia state are considering their own euthanasia legislation.
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