The historic reforms were given royal assent on December 8, the final step in a process that began with a national postal vote in September.
There was supposed to be a 30-day waiting period after couples registered to marry, with the first weddings expected on January 9.
But some sought an exemption due to their circumstances, and the first ceremonies went ahead today, one in Sydney and one in Melbourne.
"Australia's first legal same-sex marriage has just taken place. Congratulations Amy and Lauren," Equal Marriage Rights Australia announced on its Facebook page.
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A photo showed Price and Laker dressed in traditional white gowns and holding hands as they said "I do" on a glorious Sydney day.
Among hundreds of comments on the Facebook page, Paul Antoine said: "Now... has the country collapsed? NOOO!! Two women have just shown their love. Pretty simple, but nonetheless special in my view!"
Jason Chapman added: "Relentless dedication from so many over the last fifty years have led us to enjoy this beautiful moment of equality. Congratulations ladies."
The bill was introduced in parliament by the conservative government after Australians in November endorsed the reforms in a contentious voluntary postal vote.
Nearly 80 per cent of eligible voters took part in the poll, and almost 62 per cent of those who voted chose "yes" on their ballots.
Fairfax said Price and Laker had originally intended to hold a commitment ceremony at the British consulate because Price was from Wales.
Melbourne's Amy and Elise McDonald, aged 36 and 28, reportedly only got permission to marry this morning, gaining an exemption for similar reasons, according to the Herald Sun newspaper.
They were allowed to have a legal marriage on financial grounds and because their families had travelled from overseas.
Same-sex marriage is now recognised in more than 20 countries, of which 16 are in Europe.
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