The ODI series will start from September 17.
"James is a solid one-day campaigner and is very familiar with subcontinent conditions, coming off a very good tour of Sri Lanka a year ago", chief selector Trevor Hohns said.
Allrounder Moises Henriques, as well as injured quartet Chris Lynn, John Hastings, James Pattinson and Mitchell Starc, are the five omissions from the squad that was named for the Champions Trophy squad in June.
Australia will arrive in India on September 17 for five one-day internationals and three Twenty20 matches, but Starc has been ruled out with selectors hoping the extra rest will help ensure he's available for the five-test Ashes series beginning late November in Brisbane. The tour will feature five ODIs and three T20Is, with the Australians naming 14 and 13 man squads respectively.
Faulkner has been called back keeping his vast experience in the subcontinent courtesy his Indian Premier League (IPL) stints while Coulter-Nile has also impressed for his IPL franchisee in recent times.
The selectors have also named Western Australia paceman Jason Behrendorff in the T20 squad following his return from an injury setback, along with veteran all-rounder Dan Christian and Tasmania wicketkeeper Tim Paine.
"Nathan brings raw pace to the side with good variation", selector Trevor Hohns said of Coulter-Nile's selection.
Cricket Australia (CA) is upbeat Starc will return during October's domestic one-day competition, the dates of which are set to be announced early next week. "It is great to see him back from injury and we are hopeful he will have a big impact in this series".
With the Champions Trophy done and dusted all countries have now turned their focus to the 2019 World Cup in England, and with the showpiece tournament in mind there are no surprises Australia have added some youth to their squad, while also providing second chances and further opportunities to some more senior players. Skipper Steven Smith will be leading the side whereas David Warner will be the vice-captain.
"Dan is a very experienced all-rounder who can be a very unsafe batsman".
"We believe the panel has selected a strong squad to face the tough Indian conditions that has the right mix of pace and spin", Hohns said.
Cummins and Hazlewood will join captain Steve Smith, David Warner, Glenn Maxwell, Matthew Wade, Ashton Agar and Hilton Cartwright in travelling from Bangladesh to India to link up with Australia's one-day squad.