BBC broke the news of Peaches' death on Monday evening (7 April) and quoted a statement from Kent Police describing the death as "sudden and unexplained".
Peaches' father Bob Geldof paid tribute to her in a statement, saying: "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. 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."
According to police, they were called to an address in Kent after receiving a "report of concern for the welfare of a woman". Peaches was pronounced dead by South East Coast Ambulance Service.
No further information has been released.
The full statement read: "Police were called at 1:35pm on 7 April 2014 to an address near Wrotham following a report of concern for the welfare of a woman. A woman aged 25 was pronounced dead by South East Coast Ambulance Service. At this stage, the death is being treated as an unexplained and sudden death. Officers are working to establish the circumstances around the death."
Peaches was last seen in public at the F&F fashion show at Somerset House, London on 3 April.
She had been on Twitter just 23 hours before her death was reported. Her last post was an Instagram throwback picture of herself and mother Paula Yates, which she uploaded with the simple caption: "Me and my mum."
Peaches lost her mother when she was just 11.
Peaches leaves behind musician husband Thomas Cohen and sons Astala, one, and Phaedra, who turns one on 24 April.
A devastated Thomas issued a brief statement following his wife's death, saying: "My beloved wife Peaches was adored by myself and her two sons. I shall bring them up with their mother in their hearts everyday. We shall love her forever."
In his statement, Peaches' father Bob added: "Tom and her sons Astala and Phaedra will always belong in our family, fractured so often, but never broken."
Peaches Geldof: Her life in pictures
Copyright: Rex Features Dennis Stone