Ireland's new laws on gay marriage will be enacted by the end of July, with the first ceremonies likely in the autumn.
The country becomes the first in the world to bring the change in by popular vote, with 62 per cent of the electorate backing it.
Australia's political leaders on Sunday rejected the idea of a referendum on gay marriage following Ireland's successful vote.
When questioned on Sunday about whether Australia should have a referendum on the issue, Prime Minister Tony Abbott said it's a matter to be resolved in parliament.
Leader of the opposition Bill Shorten also supports a vote in parliament but is pushing for Tony Abbott to allow a conscience vote within his own party.
In 2012 the House of Representatives overwhelmingly voted against legislation that would allow same sex couples to marry.
Forty two MPs voted in support of the bill while 98 voted against.
Ireland's new laws on gay marriage will be enacted by the end of July, with the first ceremonies likely in the autumn.
Ireland's overwhelming support for gay marriage is a message to the world, UN secretary general Ban Ki-moon said.
Billie asked girlfriend Kate to marry her at a count centre in Limerick moments after the result was announced.