The all-Democratic state Senate voted 23-2 to pass the measure that has already cleared the House.
It allows doctors to fulfill requests from terminally ill patients for prescription medication that will allow them to die.
The governor said he will sign the bill, which would make Hawaii the sixth state to legalise the practice, plus Washington DC.
The legislation includes safeguards intended to prevent abuse, but opponents said it puts the poor, elderly, sick and disabled at risk.
Politicians heard hours of impassioned testimony from advocates and opponents.
Doctor-assisted deaths are legal in California, Colorado, Oregon, Vermont, Washington state and the District of Columbia. Last year, the Hawaii Senate approved similar legislation, but the state House voted it down.
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