Bob Geldof was informed of his 19-year-old daughter's plans just before the short ceremony took place.
The surprise marriage followed a whirlwind romance between Geldof and American Max Drummey, singer in indie band Chester French.
She and her new husband, 23, were together for little over a month before tying the knot.
The US nuptials came less than a month after Geldof was resuscitated by a friend when she passed out in her London flat.
A spokesman for Geldof said her father was told of the wedding shortly before it took place and gave the union his blessing despite not being able to walk his daughter down the aisle.
Geldof first met her new husband - a Harvard anthropology graduate - a year ago.
But their relationship blossomed last month after Drummey's band played at the iTunes festival in London, where Geldof hosted the ITV coverage.
The marriage had the full support of the couple's family and friends, including her ex-boyfriend, singer Faris Badwan, the spokesman said.
The spokesman added: "The couple had not intended to publicise their marriage, but decided to confirm the event due to mounting media speculation."
Geldof's parents - rock star-turned-philanthropist Bob and the late Paula Yates - also married in Las Vegas.
But the couple, who wed in the 1980s, later separated.
Rev Steven Fabretti, who performed the 15-minute ceremony, told The Sun Geldof and Drummey looked "very happy together".
"They held hands and looked eye-to-eye - with him still wearing sunglasses - during the ceremony.
"They looked very happy together. I remember the bride looked very young and pale and quite angelic," he told the newspaper.
Although press interest in Peaches daughter has tended to focus on her penchant for partying and a series of rocker boyfriends, she has carved out a niche for herself presenting a number of youth TV programmes, including Peaches Geldof: Teenage Mind and A Beginner's Guide to Islam.
Last month she was forced to deny rumours she had suffered a drug overdose after she passed out at her home.
A friend gave her mouth-to-mouth resuscitation at her north London flat when she stopped breathing.
An ambulance was called, although she did not require hospital treatment.
Her mother was found dead at the age of 40 from an overdose at her home in west London in September 2000.