The warm-up game precedes the Tri-Series between England, India and the Aussies, which itself comes just ahead of the World Cup.
Maxwell, who played for Hampshire last summer, and Cummins will be hoping to impress with places in the Australia World Cup team up for grabs.
The team will be captained by former Test batsman Mike Hussey.
Australia Prime Minister Tony Abbott said: ???It gives me great pleasure to announce the squad to play England in this month???s Prime Minister???s XI match.
???This team is an exciting mix of emerging talent and big name players.
???This fixture promises to be an exciting day in what???s shaping as a memorable summer of cricket in Australia.”
National Selection Panel Chairman Rod Marsh said: ???This match is a special fixture on the Australian cricketing calendar and a magnificent tradition. Mike Hussey will lead the team well and is a great drawcard, as is local boy Jason Behrendorff, who has been in fantastic form this summer across all three formats.
???Fans will also be looking forward to seeing Pat Cummins and Glenn Maxwell in action. Pat has been in excellent form, bowling fast for the Sydney Thunder this summer, while Glenn can electrify the crowd with his daring and aggressive stroke play.
???Eighteen-year-old batsman Jake Doran is in the team, and he will also take the gloves. I think we all realise what a great talent Jake is, and his selection will provide another opportunity for him to continue his development.
???We are also excited about 22 year old batsman Lega Siaka, contracted to the Melbourne Renegades in the KFC T20 Big Bash League. Lega scored a century for Papua New Guinea in their first ever One-Day International series in November when they defeated Hong Kong, and he is a confident young batsman who will excite the fans. His selection highlights PNG???s growth as a cricketing nation.???
Team: Mike Hussey (captain), Cameron Bancroft, Jason Behrendorff, Matt Condon, Pat Cummins, Jake Doran, Peter Handscomb, Simon Mackin, Glenn Maxwell, David Moody, Lega Siaka. 12th man: Mac Wright.