Police have confirmed that Peaches was declared dead on Monday, 7 April after emergency services were called to her home in Kent. Her death has been described as "sudden and unexplained". No further details have been released.
Peaches leaves behind husband Thomas Cohen and sons Astala, nearly two, and Phaedra, who turns one later this month.
A statement issued by Bob and his family on Monday night read: "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."
The statement added: "Tom and her sons Astala and Phaedra will always belong in our family, fractured so often, but never broken."
Bob's statement was signed by himself, girlfriend Jeanne, and his daughters Fifi, Pixie and Tiger.
Peaches' mother Paula Yates passed away when Peaches was 11.
Peaches Geldof: Her life in pictures
Copyright: Rex Features Dennis Stone