Governor-General Peter Cosgrove signed the same sex marriage bill into law on Friday, a day after MPs overwhelmingly approved a historic bill.

"So it is all done," said Prime Minister Malcolm Turnbull, "It is part of the law of the land."

The law comes into force on Saturday - thus, the first same sex marriage ceremonies in Australia will begin on 9 January because couples have to give a month's notice of their intention to wed.  But couples who were married overseas will have those marriage recognized in Australia as of midnight.

Labor leader Bill Shorten said the new law spoke for a modern, "inclusive and fair" Australia.  Attorney General George Brandis told the ABC that he had celebrated with his Labor counterpart Penny Wong last night.

"I saw Senator Wong at an event and we did have a drink, which doesn't happen very often, but it was a completely non-partisan achievement," Senator Brandis said.  "This is not owned by the Liberal Party or the Labor Party or any political party," he added, "It is owned by the Australian people."