Eoin Morgan will captain the side in Cook's absence, while pace bowlers Chris Jordan and Jamie Overton are included in an England squad for the first time.
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Michael Carberry, Gary Ballance and Boyd Rankin, who are yet to make their ODI debuts for England, have also been selected.
"Following a very intense period of cricket this summer we have decided to rest a number of senior players which will allow them to recover from a heavy workload over the last three months and to prepare for the tour of Australia which begins in eight weeks," national selector Geoff Miller said in a statement.
England have named a separate squad for a one-off ODI against Ireland on September 3, for which Kevin Pietersen, Joe Root and Jonathan Trott will also be rested before returning for the Australia matches.
They have been replaced by Ballance, James Taylor and Danny Briggs.
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The first ODI against Australia is at Headingley on September 6.
Squad for Ireland match: Eoin Morgan (captain), Gary Ballance, Ravi Bopara, Danny Briggs, Jos Buttler, Michael Carberry, Steven Finn, Chris Jordan, Jamie Overton, Boyd Rankin, Ben Stokes, James Taylor, James Tredwell, Luke Wright.
Squad for Australia matches: Eoin Morgan (captain), Ravi Bopara, Jos Buttler, Michael Carberry, Steven Finn, Chris Jordan, Jamie Overton, Kevin Pietersen, Boyd Rankin, Joe Root, Ben Stokes, James Tredwell, Jonathan Trott, Luke Wright.
Schdule (England vs Australia limited overs series):
| Aug 29 | First T20I (D/N) | Southampton | 2300 IST |
| Aug 31 | Second T20I | Chester-le-Street | 1900 IST |
| Sep 6 | First ODI | Leeds | 1445 IST |
| Sep 8 | Second ODI | Manchester | 1445 IST |
| Sep 11 | Third ODI (D/N) | Birmingham | 1830 IST |
| Sep 14 | Fourth ODI | Cardiff | 1445 IST |
| Sep 16 | Fifth ODI (D/N) | Southampton | 1830 IST |
Image: Eoin Morgan
Photograph: Philip Brown/Reuters