Australia's first same-sex marriages have taken place at ceremonies in Sydney and Melbourne.

Two couples were granted an exemption to be able to marry before January 9.

Lauren Price, 31, and her partner Amy Laker, 29, walked down the aisle today, becoming the first same-sex couple to be married in Australia.

The ceremony in Camden, in Sydney's south-west, was attended by 60 relatives and friends who flew from around the world to be part of the special day.

The crowd cheered when celebrant Janice Bradley pronounced them a married couple.

Ms Bradley says she never thought she would be the first celebrant to marry a same-sex couple in Australia.

She added that she was happy for Amy and Lauren.

The couple was granted a rare exemption so they could marry more than three weeks before other same-sex couples.

They had already planned to marry at the British Consulate under UK law, but after the postal survey result they decided to marry under Australian law.

They asked for an exemption from the notice period due to the fact Lauren's Welsh family had already booked tickets for the ceremony.

"We went to Births, Deaths and Marriages and made our case," Lauren said.

"It was the longest ten minutes of our lives and Amy cried when they said yes. It's was so wonderful."

The exemption was granted on financial grounds, citing the travel costs of the couple’s relatives.

A same-sex couple in Melbourne was also married today after also being granted an exemption.

A surge of same-sex marriages is expected from January 9, the first official day same-sex marriages will be allowed.