Laws on same-sex marriage are due to be debated this week when the Dáil returns from summer break.
The first same-sex marriage ceremonies could take place by the end of the year.
Ireland voted in favour of same-sex marriages in May's referendum, but the legislation has been delayed by legal challenges.
Senator Katherine Zappone married Ann Louise Gilligan in Canada in 2003 and the couple intend to renew their vows in Ireland.
Senator Zappone said: "In the marriage bill starting in the Dáil this week, same-sex couples who have contracted marriage in another State...are automatically recognised once this passes and the Act commences.
"The wonderful thing about it too is that it's retrospective, so the marriage is recognised not just from the day of commencement of the Act, but from the day of your marriage."