Japan-based Nabbout rejoins the 23-man squad after injuring his shoulder at the World Cup in Russia, while Huddersfield Town playmaker Mooy returns after missing the 4-0 friendly win over Kuwait last month.
Austria-based midfielder James Jeggo is a surprise selection and will hope to secure his first international cap after making a number of squads under former coach Ange Postecoglou.
Scotland-based forward Martin Boyle has been included and will be eligible to play against Asian heavyweights South Korea in Brisbane next week after receiving his international clearance.
His Hibernian team mate Jamie Maclaren has also been recalled as Arnold looks to shape a new forward line following the retirement of veteran striker Tim Cahill and the loss of young talent Daniel Arzani to a serious knee injury.
"These two games are very important," Arnold told reporters in Sydney on Thursday.
"I'm very keen to see us play against Korea in Brisbane ... It's all about our new style we're implementing and the new principles of play we've worked hard on."
Arnold has also named an additional four train-on players to join the squad for a training camp before the South Korea friendly on Nov. 17 at Lang Park.
Australia then play Lebanon in a friendly in Sydney on Nov. 20 which also doubles as a farewell match for Cahill.
Squad:
Mustafa Amini, Aziz Behich, Martin Boyle, Milos Degenek, Alex Gersbach, Jackson Irvine, James Jeggo, Tomi Juric, Matthew Jurman, Robbie Kruse, Mitch Langerak, Mathew Leckie, Massimo Luongo, Awer Mabil, Jamie Maclaren, Mark Milligan, Aaron Mooy, Andrew Nabbout, Josh Risdon, Tom Rogic, Mathew Ryan, Trent Sainsbury, Danny Vukovic
Train-on players:
Thomas Deng, Craig Goodwin, Rhyan Grant, Dimi Petratos
(Reporting by Ian Ransom in Melbourne; Editing by Greg Stutchbury)
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