Two same-sex couples have made history by becoming the first to wed under Australian law.

Lauren Price, 31, and Amy Laker, 29, exchanged vows in Sydney on Saturday, one week after the new laws came into effect.

The ceremony took place in front of 65 guests at a ceremony in Camden in Sydney's south-west.

The first same-sex weddings were expected to happen from January 9 next year but some couples have been eligible for exemptions allowing them to wed earlier.

Ms Price and Ms Laker successfully obtained a waiver exempting them from the one-month waiting period of a wedding because their families were travelling from Wales to be there.

Friends and family of the couple flew from around the world to be part of the day.

Meanwhile, Amy and Elise McDonald's surprise wedding took place in Melbourne's Carlton Gardens on Saturday in front of about 60 unsuspecting guests.

The couple told the Herald Sun they had planned a commitment ceremony for this weekend but realised at the eleventh hour that they could be eligible for an exemption from Births, Deaths and Marriages on financial grounds.

Elise McDonald's parents had flown from Asia for the ceremony, while other siblings had made the long journey from the United Arab Emirates.

"We were always going to have a ceremony but to have it legalised is very special," she told the Herald Sun.

One couple's race against time

Another Melbourne couple, Cas Willow, 53, and Heather Richards, 56, will also be among the first to wed with their wedding slated to take place on Monday.

The couple are in a race against time because Ms Willow has breast cancer, which has spread to her brain.

Cas Willow (left) and Heather Richards have been together for 17 years. ( AAP: Supplied )

Births, Deaths and Marriages gave the couple permission to wed on Monday in light of Ms Willow's circumstances.

"I don't even know if I'll make it to Christmas, let alone January 9, so they allowed us to get married early," Ms Willow told AAP on Friday.

The pair said staff from the Peter MacCallum Cancer Centre, where Ms Willow is receiving treatment, suggested they arrange a fast-tracked wedding hosted by the hospital.

"We are thrilled to support the celebration of Cas and Heather's marriage," the hospital's chief executive Dale Fisher said.

The couple got engaged when federal Parliament legalised same-sex marriage, rather than have a commitment ceremony as it "just wasn't the same".

"It means our relationship won't just be tolerated, it will be accepted," Ms Richards said.

ABC/AAP