The pair signed official partnership documents before a registrar and two witnesses in a private ceremony at the Belfast City Hall, to a recording of Dolly Parton’s 1872 hit, ‘Touch Your Woman.’
Ms Close, 32, grew up in a Catholic family north of Belfast.
She met her partner, Ms Sickles, a 27-year-old American, in New York four years ago.
They became engaged in a ceremony in New York in October, but chose to register their partnership in Britain to make it easier for Ms Close to eventually immigrate to the United States.
“For us, this is about making a choice to have our civil rights… acknowledged and respected and protected as any human being,” Ms Close and Ms Sickles said before stepping inside the hall.
“We feel very privileged and blessed to be here doing this. We look forward to having a wonderful day,” Ms Sickles said.
Afterwards, the couple brushed past a group of about 40 protesters on their way to a waiting ribboned Hackney taxi, saying they were “delighted” and hoped there would be “many more.”
Two other couples then followed Ms Sickles and Ms Close ‘down the aisle’.
But the UK’s first civil partnership was held in Brighton on December 5, just hours after the Civil Partnership Act became law.
A 15-day waiting period was waived to allow Christopher Cramp to formally recognise his relationship with Matthew Roche, suffering inoperable lung cancer, at his hospice bedside.
Mr Roche died the next day.
Scotland is due to hold its first ceremonies on December 20, with England and Wales following a day later.
At least 1,200 ceremonies have reportedly been scheduled across Britain, according to figures from councils compiled by BBC’s online news.
The long-awaited union of popstar Elton John with his partner David Furnish is set to be among the first wave of the British ceremonies.
Campaigners say the new civil partnership institution will end inequalities suffered by same-sex couples.
While not technically constituting a marriage, where the signing of a legal partnership must take place publicly and are not permitted in a church, civil partnerships offer gay couples similar rights regarding tax, inheritance and social welfare provisions.
Opponents, though, argue that the move goes too far.
“While the word marriage is not used in the ceremony, we do believe it is deemed and received by those taking part to be one thing only – marriage,” Free Presbyterian Reverend David McIlveen told BBC television from the protest picket line outside Belfast City Hall.
“Homosexuality in the Bible is described as an abomination. You cannot place something that is unnatural on the same level as something that is natural,” the Protestant minister added.
Britain now joins Canada, Belgium, the Netherlands and Spain in recognising some form of gay union by law.