The 25-year-old model and columnist - who has two sons, Astala, 23-months, and Phaedra, 11-months, with husband Tom Cohen - passed away at her home in Kent, England on Monday afternoon (07.04.14).
'X Factor' judge Sharon, whose husband, Ozzy Osbourne, and their children Jack and Kelly Osbourne have all battled addictions in the past, wrote on Twitter: ''Devastated about @peaches_g. Sending condolences & respect to the Geldof family. It's unimaginable what they must be going through right now''
'Fashion Police' co-host Kelly, a close friend of Peaches' younger sister Pixie Geldof, 23, later tweeted: ''Words seem inadequate 2 express the sadness I feel about @peaches_g death We are here 2 support U @pixiegeldof1 stay strong my little Pepsi! (sic)''
Duran Duran frontman Simon Le Bon, who acted as Sir Bob Geldof's best man when he married Peaches' mother Paula Yates in 1986, also shared his condolences on the social media site, writing: ''How sad to hear about Peaches. Lovely, wild girl that she was. To Tom & the boys, to Bob & family, our deepest sympathy & support.''
TV presenter Paula died of a heroin overdose in September 2000, after splitting with Bob and forming a relationship with INXS frontman Michael Hutchence, who died in 1997.
Peaches, who previously admitted drug use as a teenager but said in 2009 that she was ''sober now,'' is also survived by older sister Fifi Geldof, 31, and younger half-sister Tiger Lily Hutchence Geldof, 17.
A post-mortem is expected to take place in the next few days.