Bob wrote in the statement: 'Peaches has died. We are beyond pain. She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.’
Peaches only just celebrated her 25th birthday and leaves behind two sons Astala and Phaedra.
She has an older sister, Fifi Trixabelle, and younger sisters Pixie and Tiger Lilly.
She also leaves behind husband Thomas Cohen, who she married in 2012.
She was previously .’married to musician Max Drummey between 2008 and 2011.
The star’s last tweet was a picture of her mother, Paula Yates, who passed away from a drug overdose in 2005.
Peaches other family members are yet to comment on the news.
Celebrities have taken to Twitter to pay their respects to the star following her shocking death.
Lauren Goodger was one of the first to respond, tweeting: 'OMG RIP Peaches Geldof .. I'm in shock..my thoughts and love goes out to her family.'
McFly's Tom Fletcher also wrote: 'Just heard about Peaches Geldof. So, so awful. Really sad. Thoughts going out to her family.'