Peaches Geldof, the daughter of Irish singer Sir Bob Geldof and the late Paula Yates, has died at the age of 25.
Kent Police say they were called to an address near Wrotham following a report of concern for the welfare of a woman on Monday afternoon.
The woman, aged 25, was later pronounced dead by South East Coast Ambulance Service.
"At this stage, the death is being treated as an unexplained and sudden," said a statement from Kent Police.
Ms Geldof, a mother-of-two, was a prolific tweeter and the final message that she sent yesterday was a picture of her as a child with her mother.
Kent Police said: "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 sudden death. Officers are working to establish the circumstances around the death."
Thomas Cohen, husband of Peaches Geldof, 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 everyday. We shall love her forever. Thomas Astala and Phaedra Geldof-Cohen"
Bob Geldof 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. 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.
"Bob, Jeanne, Fifi, Pixie and Tiger Geldof."
Ms Geldof was a young girl when her mother died tragically from an overdose in 2000 after splitting with Bob Geldof and forming a relationship with INXS frontman Michael Hutchence. Hutchence died in 1997.
Tributes to Peaches Geldof have begun to pour in after news of her death emerged shortly after 6pm.
Ex-footballer Stan Collymore kicked off tributes, taking to Twitter to express his sadness at the news.
He said: "RIP Peaches Geldof. Extremely sad news."
BBC show business correspondent Lizo Mzimba also posted on the social media site to express his condolences.
He said: "Awful news. Thoughts with her friends and family."
Former Rugby star Brian Moore expressed his sympathy for Peaches' father Bob Geldof, saying: "Bob Geldof - his heart must be breaking right now - very sad."
Welsh singer Aled Jones echoed Moore's sentiments, Tweeting: "Very sad news of the death of Peaches Geldof - my thoughts and love to Bob and family x"
Businessman and Apprentice star Lord Sugar used his Twitter account to express dismay at the newsof the 25-year-old's death.
He said: "Peaches Geldof dies aged 25 . What happen there ??? That's a shock"
Former England cricket captain Michael Vaughan also addressed his comments to Bob Geldof, saying: "Thoughts are with Bob Geldof... I don't even want to imagine what he is going through..."
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 told fans on Twitter: "never knew Peaches but the loss of a life so young is a horrible thing, especially leaving behind two children".
Alexandra Burke said:" I can't believe Peaches has passed away..in feel so numb. I've never met anyone so kind before. She was a beautiful person".
By Helen William
Peaches Geldof, the daughter of Bob Geldof and Paula Yates, had moved from life as a wild child in the glare of the public gaze to becoming a mother of two.
Her second child, a boy called Phaedra Bloom Forever born on April 24 2013, shares the same birth date as her late mother, author and TV presenter Paula Yates.
She was 11 years old when her mother died of a heroin overdose at 41.
In another coincidence that date - April 24 - had also been the original due date of elder son Astala Dylan Willow, now aged two. His birth was brought forward when it was decided that she should have a Caesarean.
She is the second daughter of Geldof and Yates and the granddaughter of Hughie Green. Her sisters are Fifi Trixibelle and Pixie and she has a younger half-sister named Heavenly Hiraani Tiger Lily.
In an interview with Hello magazine she said of Phaedra's unusual name: "I wouldn't be a Geldof if I didn't get stick in the press about my ridiculous choice of names. I've got to uphold the family tradition.
"We chose Bloom because my middle name is Honeyblossom and also in homage to the Nirvana album In Bloom. 'Forever' we chose purely because it sounds cool. I love his name and think he sounds like a rock star."
The 25 year-old married musician Tom Cohen, the father of her children, in 2012. Cohen plays with the band S.C.U.M.
They married at the St Mary Magdalene and St Lawrence Church in Kent, where her parents got married and where her mother's funeral were held.
She said she felt her late mother was "watching over" her as she got married.
She told Hello magazine: "I feel her presence all the time but especially today.
"Mum loved family celebrations and she would adore Tom and the fact that we've married here.
"I know that she is watching over me and feeling so happy for us."
The one-time model and journalist was previously married to rock musician Max Drummey. They married in August 2008 but separated in 2009.
Her last tweet was a photograph of her and her late mother yesterday at 10.17am.