Cheika has also opted to only take two specialists hookers - team captain Stephen Moore and Tatafu Polota-Nau, with James Hanson left behind.
Horwill, White and Hanson have been named in extended squad that will travel to Chicago for a Test against the USA on September 5.
Others in the extended squad, who will be on standby in case of any tournament-ending injuries occur, are forwards Sam Carter, David Dennis, Tetera Faulkner, Scott Higginbotham and backs Samu Kerevi, Christian Lealiifano and Taqele Naiyaravoro. The bolter in the squad is Melbourne Rebels prop Toby Smith.
Wallabies World Cup squad:- Backs: Israel Folau, Adam Ashley-Cooper (vice-capt), Rob Horne, Drew Mitchell, Henry Speight, Joe Tomane, Tevita Kuridrani, Kurtley Beale, Matt Giteau, Matt Toomua, Quade Cooper, Bernard Foley, Will Genia, Nick Phipps.
Forwards: Wycliff Palu, David Pocock, Michael Hooper (vice-capt), Ben McCalman, Sean McMahon, Scott Fardy, Kane Douglas, Dean Mumm, Rob Simmons, Will Skelton, Stephen Moore, Tatafu Polota-Nau, Greg Holmes, Sekope Kepu, Scott Sio, James Slipper, Toby Smith.