Samuel Rutherford, the executive director of A Gender Agenda, a community organisation which advocates for transgender, gender-diverse and intersex people, said he was "delighted" with the decision.
A Gender Agenda intervened in the case as amicus curiae, or a friend of the court.
Mr Rutherford said he was especially pleased that the court had recognised "non-specific" as the most appropriate term for a person who is neither male nor female.
He said while the decision would only be binding on NSW, it would be "highly influential" on other jurisdictions.
The ACT last month became the first Australian jurisdiction to make provision for people to be recognised as neither male nor female. It also removed the requirement for surgery for people who wish to change their sex registration.
Mr Rutherford added that Wednesday's decision would be a powerful affirmation of the identity of many people for whom the decision was not personally relevant.
''It's actually a really big thing to have a statement from the High Court saying that you exist and that the law should recognise you," he said.
Anna Brown, the Director of Advocacy & Strategic Litigation for the Human Rights Law Centre, which assisted A Gender Agenda with the case, said the judgment was a victory for the growing numbers of gender diverse people across Australia.
"Sex and gender diverse people face problems every day accessing services and facilities that most Australians can use without thinking twice. It's essential that our legal systems accurately reflect and accommodate the reality of sex and gender diversity that exists in our society, and the High Court has taken an enormous leap today in achieving that goal," said Ms Brown.
Read more here