A postmortem on Peaches Geldof, 25, will be carried out in the coming days, Kent police said, as detectives continue to investigate the "unexplained" fatality.
Police said Peaches was pronounced dead at her house in Kent, after they were called there yesterday afternoon.
"The death is being treated as a non-suspicious, but an unexplained sudden death," a police spokesman said. "Officers are working to establish the circumstances and will be compiling a report of their findings for the coroner."
Kent police declined to confirm or deny reports that no drugs or suicide note were found at the home, where detectives were continuing their inquiries, the Guardian reported.
Peaches was the second daughter of Bob Geldof and the late TV presenter Paula Yates.
Her mother, Paula Yates, died from an accidental heroin overdose in 2000 when Geldof was 11. Her transformation from wild child to devoted mother seemed to have been sealed when Mother & Baby magazine announced in February that she was to be its new columnist.
Peaches was married to the musician Thomas Cohen and they had two sons: Astala, who is almost two, and 11-month-old Phaedra.
In a family statement issued last night, Bob Geldof, 62, said: "She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.
"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. How sad that sentence is. Tom and her sons Astala and Phaedra will always belong in our family, fractured so often, but never broken."
On his wife's death, Cohen said: "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."
Her final tweet, posted on Sunday, linked to an Instagram picture of her, as a baby, in her mother's arms. The caption simply read: "Me and my mum."
Peaches embarked on a media career at the age of 15, when she began writing a column for Elle magazine.
She left home at 16 and went on to contribute to the Telegraph and the Guardian, as well as TV shows including ITV2's OMG! with Peaches Geldof.
She also worked as a model and, just last week, attended a launch for Tesco's F&F clothing range in London.