Their condition must be expected to cause death within a year, they must have decision-making capacity, and proceed without coercion.
Deputy Premier Steven Miles says the law won't make terminally ill Queenslanders' deaths any less tragic, but it will ease their pain and suffering.
"It has been a very considered debate and, as many members on both sides of the house have said, it's been a very difficult debate," he told parliament on Thursday.
"But I think our goal in everything is to make sure we get this right."
Thirty MPs voted against the bill and one abstained. LNP member for Surfers Paradise John-Paul Langbroek missed the vote after being stranded by state border closures.
Many of the objectors were concerned that due to a funding shortfall for palliative care, the bill would put pressure on some patients to end their lives.
"Will this government provide a guarantee that people will get access to quality integrated palliative care services wherever they live in Queensland, when they have a terminal diagnosis, and not just in the last few months of life," Liberal National Party MP Fiona Simpson said.
But Mr Miles said palliative care and voluntary assisted dying were complimentary policies, which gave more options to terminally ill people.
"Members do not have to choose between palliative care and voluntary assisted dying, they are not competitive," he told parliament.
"They, in fact, can and do operate, side by side and by continuing to harp on as though it is a choice you're attempting to demand members make a false choice. And it is indeed a false argument."
Parliament did not pass any of Deputy Opposition Leader David Janetzki's 54 proposed amendments, which he said would improve safeguards for conscientious objectors and reporting processes.
The scheme will be operating from January 2023, meaning Queensland will become the fifth jurisdiction in Australia to legalise euthanasia.
Voluntary-assisted dying is legal in Victoria, Western Australia, South Australia and Tasmania.
Readers seeking support and information about suicide can contact Lifeline 24 hours a day online and on 13 11 14. Other services include the Suicide Call Back Service on 1300 659 467, Beyond Blue and Kids Helpline (for people aged five to 25) on 1800 55 1800.
The Australian Centre for Grief and Bereavement can be contacted on 1800 642 066.