The landmark legislation was approved after more than 100 hours of gruelling debate - including two all-night sittings.
The law means terminally ill patients in Australia's second-most populous state will have the right to request a lethal drug from mid-2019.
They must be aged at least 18 and have less than six months to live.
"I'm proud today that we have put compassion right at the centre of our parliamentary and our political process," said state Premier Daniel Andrews.
