O'Connor: Held closed ceremony three weeks ago
O'Connor, best-known for hit Nothing Compares 2 U, married Press Association reporter Nick Sommerlad three weeks ago.
Sommerlad, 27, met O'Connor, 35, in February after being introduced by a mutual friend when he began working in Dublin.
"We fell for each other very quickly," he said.
Proposal
"Both of us have been out with various people in the past, but we are both very happy now."
Sommerlad, a distant relative of Queen Silvia of Sweden, proposed to the mother-of-two in June.
O'Connor has had relationships with a number of journalists in the past. She recently split from diarist Dermot Hayes, her boyfriend of two years.
Prior to that she was in a relationship with Irish Times columnist John Waters, who fathered five-year-old daughter, Roisin.
Difficult upbringing
She has been married once before, to writer John Reynolds with whom she has a 13-year-old son, Jake.
Born in Dublin in 1966, O'Connor had a difficult upbringing. Her parents divorced when she was eight years old, and she said that her mother, killed in a 1985 car crash, abused her.
Expelled from Catholic school, she was then put in a boarding school. At the age of 15, while singing at a wedding, she was spotted by drummer Paul Byrne of In Tua Nua, an Irish band acknowledged as an influence on U2.
O'Connor left boarding school to focus on a career in music. In 1986 she made her recorded debut on the soundtrack of The Captive, with U2's The Edge.
O'Connor was one of the most controversial singers of the 1990s. In the United States, Frank Sinatra threatened to "kick her ass" when she refused to perform in New Jersey if the American national anthem was played.
She also tore up a picture of the Pope during an appearance on an American TV show, and declared herself gay.