MPs voted in favour of the bill 59 to 31, with many cheering and clapping after the bill was passed.
Health Minister Brad Hazzard, one of 15 co-sponsors of the bill brought by independent MP Alex Greenwich, urged his colleagues to support the draft laws when he kicked off debate on Tuesday.
"The people's representatives in the NSW parliament have the opportunity to right a wrong that was enacted into law 119 years ago," he said.
But several MPs raised concerns over late-term abortions and a provision relating to conscientious objection by medical practitioners, as well as the amount of time given to consult on the bill.
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न्यु साउथ वेल्समा अब गर्भपतन अपराध नहुने, नयाँ कानून बन्यो