Cheika made six changes to the side that suffered a 24-19 loss to Scotland in Sydney last week and more could follow when he names his reserves on Friday.
The 34-year-old Moore will become the 10th most-capped international player when he makes his 120th Wallabies appearance at his Queensland Reds home ground on Saturday.
Meanwhile, Brumbies prop Scott Sio and lock Rory Arnold will be joined by Waratahs number eight Lopeti Timani to complete the four changes to the home scrum.
The quartet are included at the expense of rookie prop Tom Robertson, hooker Tatafu Polota-Nau, lock Sam Carter and number eight Scott Higginbotham.
In the backs, veteran centre Rob Horne returns to the Wallabies starting lineup for the first time in 12 months, while Melbourne flyer Sefa Naivalu gets the chance to add to his six tests on the wing.
The pair replace Tevita Kuridrani and Eto Nabuli as the Wallabies hope to extend an unbeaten record against Italy to 17 matches.
Australia: 15-Israel Folau, 14-Dane Haylett-Petty, 13-Rob Horne, 12-Karmichael Hunt, 11-Sefa Naivalu, 10-Bernard Foley, 9-Will Genia, 8-Lopeti Timani, 7-Michael Hooper, 6-Ned Hanigan, 5-Adam Coleman, 4-Rory Arnold, 3-Allan Alaalatoa, 2-Stephen Moore (captain), 1-Scott Sio.
Replacements: To be named on Friday.
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
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