The Australian Capital Territory has become the first jurisdiction in Australia to legalise same-sex marriage.

The bill was passed by just one vote.

Under the law, same-sex couples from across Australia will be able to marry in the ACT, which includes the capital Canberra, after giving four weeks' notice.

Chief Minister of the Australian Capital Territory Katy Gallagher told parliament that there was "no longer any excuse if there ever was to discriminate against same sex couples in our community".

"They are our children, our parents, our brothers, our sisters, our leaders ... more than anything, they are our equals," she said to cheers from the crowd in the parliamentary gallery.

The national government, led by conservative Prime Minister Tony Abbott, is expected to challenge the laws in the High Court of Australia, despite 11th hour amendments made to strengthen the marriage equality bill against any challenges.

Laws to legalise same-sex marriage failed to pass in Australia's national parliament in September 2012.

New Zealand became the first country in the Asia-Pacific region to legalise same-sex marriage in April this year.