Peaches Geldof, the daughter of Bob Geldof and the late Paula Yates, has been found dead at her home in Kent at the age of 25.
The death of the mother-of-two, who had worked as a DJ, model and television personality, is being treated as unexplained and sudden by police.
Her father said: "Peaches has died. We are beyond pain. She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us. Writing 'was' destroys me afresh. What a beautiful child.
The picture Geldof posted with her mother
"How is this possible that we will not see her again? How is that bearable? We loved her and will cherish her forever.
"How sad that sentence is. Tom and her sons Astala and Phaedra will always belong in our family, fractured so often, but never broken."
Her husband Tom Cohen said in a statement: "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 everyday."
Peaches Geldof with Tom Cohen
Police were called to her house in Wrotham at 1.35pm after receiving a report of concern for the welfare of a woman.
She was pronounced dead by South East Coast Ambulance Service.
In her last message on Twitter, she posted a picture of her as a child with her mother, who died of a heroin overdose in 2000.
Geldof's friend Lily Allen tweeted: "My thoughts are with the Geldof's at this awful time. I hope they get to grieve in peace. Peaches, rest in peace gorgeous girl."
Bob Geldof said Peaches will be "cherished forever"
Singer Ellie Goulding said: "Even if you think you've got it all figured out, some things still can't be explained or understood. Two beautiful children. RIP Peaches."
Rapper Professor Green wrote: "Never knew Peaches but the loss of a life so young is a horrible thing, especially leaving behind two children."

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