"We can confirm that the body has been released to the family for funeral arrangements to be made," a spokesman for North West Kent coroner Roger Hatch said.
Officers will continue to investigate the circumstances surrounding her death, although they are not treating it as suspicious.
Peaches Geldof - a life in pictures
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Peaches' Instagram profile, which was filled with touching images of the socialite and her sons, was shut down yesterday.
Among the first to pay tribute was pop star Lily Allen, a long-time friend of the devoted mother of two sons - Astala, 23 months, and Phaedra, 11 months - with husband Thomas Cohen.
"My thoughts are with the Geldof's at this awful time," she wrote. "I hope they get to grieve in peace. Peaches, rest in peace gorgeous girl."
Ellie Goulding echoed the sentiments of many hearing the news for the first time when she wrote: "I don't believe it,' before adding: '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."
Fearne Cotton wrote: "I'm beyond shocked and saddened to hear about Peaches. Can't quite digest it. Thoughts and so much love to the family."
Sister Fifi Geldof released a family photograph in tribute to Peaches on Tuesday
"Peaches has died. We are beyond pain," he wrote. "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."
"My beloved wife Peaches was adored by myself and her two sons," said husband Thomas Cohen in a statement.
"I shall bring them up with their mother in their hearts everyday. We shall love her forever."
