The High Court ruled that not everyone should be forced to identify as a man or woman when dealing with officials, saying some people could legitimately describe themselves as gender neutral.
"The High Court... recognises that a person may be neither male nor female, and so permits the registration of a person's sex as 'non‑specific'," it said in a unanimous judgement.
The decision ended a long legal battle by sexual equality campaigner Norrie to overturn a New South Wales state edict that gender is an inherently "binary" concept involving only men or women.
"I'm overjoyed," the Sydney-based activist said. "It's been a long time from start to end but this has been a great outcome.
"Maybe people will understand now that there's more options than just the binary. So while an individual might be male or female, not all their friends might be and maybe they might be more accepting of that."
The 53-year-old, who uses only a single name, was born male and underwent gender reassignment surgery in 1989 to become a woman.
But the surgery failed to resolve the Scottish-born activist's ambiguity about sexual identity, prompting a push for the recognition of a new, non-traditional gender.
Norrie made global headlines in February 2010 when an application to the NSW Department of Births, Deaths and Marriages accepted that "sex non-specific" could be accepted for Norrie's records.
But soon afterwards the office revoked its decision, saying the certificate was invalid and had been issued in error. At the time, Norrie said the decision felt like being "socially assassinated".
That sparked a series of appeals which resulted in the NSW Court of Appeal recognising Norrie as gender neutral last year, a decision which the High Court backed on Wednesday.
The Human Rights Law Centre, which provided expert testimony in Norrie's case, said the court had "rejected outdated notions of gender" in the decision.
"Sex- and gender-diverse people face problems every day accessing services and facilities that most Australians can use without thinking twice," the centre's litigation expert Anna Brown said.
"It's essential that our legal systems accurately reflect and accommodate the reality of sex and gender diversity that exists in our society. The High Court has taken an enormous leap today in achieving that goal."
Brown said the decision did not mean people could simply identify themselves as "non-specific" and expect legal recognition.
Under the law, only a person who had undergone gender reassignment surgery could nominate themselves as "non-specific" after presenting medical evidence to back up their claims, she said.
Brown added that it remains unclear who gender-neutral people would be able to marry.
"No one has actually looked at that question legally," she said, adding that there were few international precedents for the decision.
In most states across Australia same-sex couples can have civil unions or register their relationships, but the government does not consider them married under national law.
Germany last year passed a law allowing babies born with characteristics of both sexes to be registered as neither male nor female.
Several countries including Australia, Germany and Nepal also allow people to have an X on their passport rather than male or female, while social media giant Facebook recently moved to allow users to choose "other" gender options, such as "transsexual", "intersex" or "androgynous".
Activist group Gender Agenda said the court decision's impact went far beyond the legal system.
"Transgender, gender diverse and intersex people face high levels of stigma, social exclusion and discrimination," group director Samuel Rutherford said.
"To have the highest court in our land say the law recognises the reality of our existence is not only important in a practical way, but paves the way for achieving equality and freedom from discrimination."