Yadav and Shami were part of the test squad which blanked Sri Lanka 3-0 but were rested from the subsequent five-match ODI series, which the tourists also swept.
Fast bowler Shardul Thakur, who played two matches in the series and took a single wicket, was dropped from the 16-man squad for the series against Australia.
The hosts will, however, continue to be without off-spinner Ravichandran Ashwin and left-arm tweaker Ravindra Jadeja for the first three of five matches against Steve Smith's side.
Axar Patel, Kuldeep Yadav and Yuzvendra Chahal will be India's spinners as the Virat Kohli-led side continues to build toward the 50-over World Cup in 2019 in England and Wales.
"The team for the three ODIs against Australia has been selected in line with the rotation policy of the Board and accordingly R Ashwin and Ravindra Jadeja have been rested," India's chief selector MSK Prasad said in a statement.
"The team's performance during the Sri Lanka tour was outstanding and players like Axar Patel and Yuzvendra Chahal, who performed very well, are being given an extended run and this will in turn supplement our approach, to build a strong reserve strength, as we prepare for forthcoming tours."
India and Australia will play five ODIs and three T20 matches during their limited-overs series, starting with the first 50-over clash in Chennai on Sept 17.
Squad: Virat Kohli (captain), Rohit Sharma (vice captain), Shikhar Dhawan, KL Rahul, Manish Pandey, Kedar Jadhav, Ajinkya Rahane, MS Dhoni, Hardik Pandya, Axar Patel, Kuldeep Yadav, Yuzvendra Chahal, Jasprit Bumrah, Bhuvneshwar Kumar, Umesh Yadav, Mohammed Shami
(Reporting by Sudipto Ganguly; editing by Nick Mulvenney)
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