The T20I and ODI squads, captained by Eoin Morgan, feature five players, Moeen, Jos Buttler, Steven Finn, Ben Stokes and Mark Wood, who were involved in the Ashes.
England batsman Joe Root has been rested for the forthcoming limited-overs series against Australia following his exertions in the Ashes.
The 24-year-old, England's leading run-scorer in the 3-2 Ashes victory, will miss the only Twenty20 fixture against Australia and the five-match One-Day International series against the same team.
Moeen Ali returns after missing the matches against New Zealand and uncapped Essex paceman Reece Topley, 21, has also been included.
The squads, captained by Eoin Morgan, feature five players, Moeen, Jos Buttler, Steven Finn, Ben Stokes and Mark Wood, who were involved in the Ashes.
"We have made some significant progress in our limited-overs cricket this summer and the next six games allow these players to continue testing themselves against one of the very best sides in the world," national selector James Whitaker said in a statement on Monday.
"This is primarily a young group of players and the next three weeks will provide them with valuable experience as we continue to identify players who can take our limited-overs cricket forward over the next four years."
The Twenty20 will take place in Cardiff next Monday followed by the ODI series, beginning in Southampton, next month.
Australia won the 50-over World Cup earlier this year.
Twenty20 squad: Eoin Morgan (captain), Moeen Ali, Sam Billings, Jos Buttler, Steven Finn, Alex Hales, Adil Rashid, Jason Roy, Ben Stokes, Reece Topley, James Vince, David Willey, Chris Woakes.
ODI squad: Eoin Morgan (captain), Moeen Ali, Sam Billings, Jos Buttler, Steven Finn, Alex Hales, Liam Plunkett, Adil Rashid, Jason Roy, Ben Stokes, James Taylor, David Willey, Chris Woakes, Mark Wood.
