Friday's results showed 65.2% of voters supported the End of Life Choice Act 2019 coming into force as a new law.
It will allow terminally ill people, with less than six months to live, the opportunity to choose assisted dying if approved by two doctors.
The referendum is binding and the law will come into effect in November 2021.
The results do not include an estimated 480,000 special votes, including postal and overseas ballots, so the final outcome will not be confirmed until next Friday. But with such strong support, the decision is not expected to change.