The 38-year-old batsman Rohit and fellow stalwart Virat Kohli, 36, were both however named in the squad for the three-match series beginning on October 19.
Top-order batsman Gill, 26, is now Test and one-day skipper, and vice-captain of India's T20 side.
He took over the Test captaincy from Rohit starting with the series in England in the summer, earning praise for both his leadership and batting.
He led from the front, scoring 754 runs in five Tests to help India draw the keenly contested series 2-2.
Gill also leads Gujarat Titans in the Indian Premier League.
Rohit, one of India's most successful limited-overs captains, led the side to a record third Champions Trophy title in Dubai earlier this year.
He and Kohli have both retired from T20Is and Tests.
Gill's vice-captain for the Australia series will be Shreyas Iyer.
India currently top both the ODI and T20 team rankings of the International Cricket Council.
India's ODI squad for Australia
Shubman Gill (capt), Rohit Sharma, Virat Kohli, Shreyas Iyer (vice-capt), Axar Patel, KL Rahul (wk), Nitish Kumar Reddy, Washington Sundar, Kuldeep Yadav, Harshit Rana, Mohammed Siraj, Arshdeep Singh, Prasidh Krishna, Dhruv Jurel (wk), Yashasvi Jaiswal.
India's T20I squad for Australia
Suryakumar Yadav (capt), Abhishek Sharma, Shubman Gill (vice-capt), Tilak Varma, Nitish Kumar Reddy, Shivam Dube, Axar Patel, Jitesh Sharma (wk), Varun Chakaravarthy, Jasprit Bumrah, Arshdeep Singh, Kuldeep Yadav, Harshit Rana, Sanju Samson (wk), Rinku Singh, Washington Sundar.
