The bill breezed through 43 votes to 12, and the moment was met with a standing ovation in the packed public and parliamentary galleries.

Senators from various parties hugged each other and cried following the vote, with some declaring it the proudest day in their parliamentary careers.

"This is the Senate's day," Liberal senator Dean Smith said shortly after. "This is a demonstration that working across the chamber ... does deliver not just good outcomes but fantastic outcomes."

Attorney-General George Brandis said he was "so proud of Australian democracy today, more proud than I have ever been". It was a day to "rejoice in what the Australian people achieved this year", he said.

The bill must now proceed to the House of Representatives. Prime Minister Malcolm Turnbull cancelled this week's sitting of that chamber, ostensibly to wait for the Senate to finish debating the same-sex marriage bill, which was originally expected to take until Thursday.

Labor's Senate leader Penny Wong - who is gay and fought within Labor for years to change its position on same-sex marriage - said it was a day of "great celebration for so many people across this country".

"It says to so many Australians: this Parliament, this country, accept you for who you are. Your love is not lesser and nor are you. It says you are one of us," Senator Wong said.

Senator Smith, the first openly gay Liberal MP, helped drive the change within the Coalition and sponsored the final bill that passed the chamber essentially unchanged on Wednesday afternoon.

"We have seen in this debate how our Parliament is meant to work," he said. "The real question out of this debate is why isn't our Parliament like this more often?"

Parliamentarians from both sides had a conscience vote on the bill, and many chose to abstain - including Employment Minister Michaelia Cash, Assistant Social Services Minister Zed Seselja and One Nation leader Pauline Hanson.

Those who voted against the change included Resources Minister Matt Canavan, International Development Minister Concetta Fierravanti-Wells and Labor senators Chris Ketter and Helen Polley.

Various amendments to the bill - including moves to allow civil celebrants to refuse to perform gay weddings - were defeated in the Senate on Tuesday and Wednesday by a combination of Labor, the Greens, some Coalition senators and some crossbenchers.

Attorney-General George Brandis: "It is well-known that some years ago, some time ago, I was not a supporter of the plebiscite, but I am so glad it happened this way. I am so glad that we involved every man and woman in Australia in this historic decision. I am so delighted that the result was an overwhelming 'yes'. I am so grateful for the grace and decency of those who were not persuaded to change in the way that they have accepted the result."

Labor senator Penny Wong: "This day would not have come without the courage and dedication of all who have campaigned, and it would not have come without the decision of the Australian people to vote yes. And in that vote, the grace and decency of our countrymen and women shone through. And in voting yes they pushed our Parliament to do what should be done. We may be their representatives, but in this, they have been our leaders."

Resources minister Matt Canavan: “I unfortunately, cannot support this unamended bill because I do not think we have made these changes in a way which advances rights fully through this process.”

Greens leader Richard Di Natale: “Love has made its way through the Senate. It is unstoppable now through the House. This is such a great occasion. It is a great moment.”