Robyn Peoples, 26, and Sharni Edwards, 27, were due to wed at 2pm (1400 GMT) in Carrickfergus, near Belfast, after the new legislation came into effect on Monday.
It followed campaigning by Amnesty International and partner organisations in the "Love Equality" campaign, which hailed the occasion "a landmark moment for equality in Northern Ireland".
"We didn't set out to make history - we just fell in love," Edwards said ahead of the nuptials in a statement released by the campaign.
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"We are so grateful to the thousands of people who marched for our freedoms, to the Love Equality campaign who led the way, and the politicians who voted to change the law.
"Without you, our wedding wouldn't have been possible. We will be forever thankful."
Her soon-to-be wife Peoples added: "While this campaign ends with Sharni and I saying 'I do', it started with people saying 'no' to inequality. By standing together, we've made history."
British MPs in London passed legislation last July, while Northern Ireland's devolved government was suspended, to allow gay marriages and same-sex civil partnerships.
The move, which brought the province into line with the rest of the UK, was opposed by a group of local lawmakers but they failed in a last-minute bid in October to block its implementation.
London spent the intervening months drawing up new regulations to apply to the marriages and partnerships - with the first permitted to happen this week.
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In the meantime, Northern Ireland's political parties also agreed to restart power-sharing in Belfast.
Activists, British MPs including Northern Ireland Secretary of State Julian Smith, and others will celebrate the occasion at a parliamentary event in London later on Tuesday.
Sara Canning, the partner of journalist Lyra McKee who was killed by dissident republicans in the Northern Irish city of Londonderry last year, helped to campaign for the change.
"Of course, this historic moment is a little bitter-sweet. It had been our dream too. Lyra and I should have been an engaged couple now, planning our own wedding day," she said in the statement.
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