Mr Fraser, 43, and Mr Stevenson, 61, both dual British-Australian citizens, have lived together in Sydney for 19 years.
Streamers are thrown after the wedding at the consulate.
Streamers are thrown after the wedding at the consulate. Photo: Wolter Peeters
''We've waited a long time to be able to get married,'' Mr Fraser said, adding that it was ''a real privilege to be the first ones married here in NSW''.
The pair was also the first in the world to marry outside Britain under the country's marriage equality laws.
The British Consul-General in Sydney, Nick McInnes, officiated at Friday's ceremony at the consulate, in a high rise overlooking the harbour, saying it was a "momentous" occasion.
They are the first same-sex couple to marry in Australia under British law.
They are the first same-sex couple to marry in Australia under British law. Photo: Wolter Peeters
The grooms, both wearing Highland dress in a nod to their Scottish heritage, exchanged vows before an intimate gathering of family and friends.
''People ask, 'Why is it so important to get married?','' Mr Fraser said. ''It's a way to celebrate your love and your partnership, in front of your family and friends, and have that recognised by them, by your community and ultimately by the state that you live in.''
Mr Fraser said it would be ''bittersweet to be married one minute and then step outside, off British soil, and to be technically unmarried under the laws of the country where we live''.
Recognition under Australian law of same-sex marriages overseas and the impact of marriage equality laws in other countries are now the the subject of a parliamentary inquiry.
The national director of Australian Marriage Equality, Rodney Croome, said British marriage law reform ''is a reminder that marriage equality can be achieved under conservative governments''.
''This will prove that when same sex couples make solemn vows of marriage, the sky doesn't fall in,'' he said. ''It will put pressure on the Abbott government to allow a conscience vote.''
Mr Fraser said not all same-sex couples in Australia had the advantage of dual citizenship that allowed them to marry at home. ''I look forward to the day when all Australian people are able to get married on Australian soil, without having to go overseas or seek refuge in the consulate of another country,'' he said.