A post-mortem will be performed in the next few days on 25-year-old Geldof, who was pronounced dead by paramedics at her home in Wrotham, southeast of London, on Monday.
Kent Police said officers were investigating the ''unexplained sudden death,'' but did not consider it suspicious.
Peaches Geldof was the daughter of Irish musician and Band Aid founder Bob Geldof and TV presenter Paula Yates, who died of a drug overdose in 2000. She grew up in the glare of Britain's press, which reveled in the late-night antics of her teenage years.
More recently she married for a second time, to musician Tom Cohen, had two children and worked as a broadcaster and writer. She said her drug-taking years were behind her.
Bob Geldof said the family was ''beyond pain.''
''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,'' he wrote in a statement.
The death came as a shock to Britain's entertainment and fashion circles. She was a frequent attendee at fashion shows in London and New York, and was photographed just last week at a London show for the Tesco brand F&F.
Geldof's death was the lead story in many British newspapers Tuesday, with several using the last photo she posted on Twitter - of her as a toddler with her mother.
Commentators noted the tragic parallels to the life and death of Yates. In The Guardian, columnist Hadley Freeman said ''the shock of Geldof's death comes from the loss of a young woman - still only 25 - who many of us had followed since her birth, who seemed so close to finding the stability that had eluded her mother.''