No immediate cause of death was released at her home in Wrotham, Kent, southeast England, but police called it "unexplained and sudden."
Geldof was a model, television presenter and fashion writer.
Her father issued an anguished statement Monday from the family about her death.
"Peaches has died. We are beyond pain. She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us," he wrote. "Writing 'was' destroys me afresh. What a beautiful child. How is this possible that we will not see her again? How is that bearable? We loved her and will cherish her forever."
Geldof admitted to using drugs in the past, but in a 2009 interview with the Guardian newspaper said she had quit.
"'Yeah, I've taken drugs. Yes, I have had experiences, and a few of those experiences were unsavory, not ones I want to repeat, but I was growing up. I wanted the experience," she told the paper.
Geldof was born on Mar. 13, 1989 to mother Paula Yates, a popular television presenter, and Bob Geldof, who rose to fame in the late 1970s as the lead singer of the Irish punk band The Boomtown Rats.
When she 11, her mother died of a drug overdose.
"It's very, very sad. Peaches has overcome a lot in her childhood, seemed to be getting her life together. You hear something like this and words can fail you. It's just tragic, terrible news," Ray Levine, Peaches' former publicist, told Sky News.
At 16, Geldof left home and began writing columns for fashion magazines and newspapers, as well as worked as a model and television presenter.
But more often than not, British tabloids and gossip magazines focused on the more sordid details of her life, including reports that she was caught shoplifting cosmetics and claims that she used heroin.
In 2010 she was dropped from a lingerie modelling contract after photographs showing her topless and allegations that she used drugs surfaced.
Geldof had two marriages. She married Max Drummey, a vocalist with U.S. indie rock band Chester French, at a drive-thru chapel in Las Vegas, but the marriage ended after six months in 2009.
Geldof is survived by her second husband, Tom Cohen, lead singer of the defunct London punk band S.C.U.M, and two sons, 23-month-old Astala and 11-month-old Phaedra.
"My beloved wife Peaches was adored by myself and her two sons Astala and Phaedra, and I shall bring them up with their mother in their hearts every day. We shall love her forever," Cohen said in a statement.
The Associated Press contributed to this report.