Australia claimed their fifth World Cup in the 50-over game in March but since then wicketkeeper Brad Haddin and Test captain Michael Clarke have announced their retirement from the format.
Fast bowlers Mitchell Johnson and Josh Hazlewood are also being rested after Australia’s unsuccessful Ashes campaign against England, which followed a Test series in the West Indies.
“The squad we have selected has a few fresh faces in it as well as some experienced players that will provide us with the right balance,” said selectors’ chairman Rod Marsh.
Marsh said Burns, 25, had impressed while playing in India for Australia A, where last week he blasted 154 from 131 balls against India A in Chennai.
Burns proved he was “a very capable young batsman who has experience opening”, said Marsh.
Stoinis, 25, was considered a handy all-rounder to replace James Faulkner who was not considered for the series after being convicted of drink-driving in England last month.
Left-arm spinner Agar, who scored a memorable 98 in his Test debut against England in 2013, also hit form in India after returning from shoulder surgery, Marsh said.
Matthew Wade takes over the wicketkeeping position from Haddin and will play his first ODI since November 2014 while Steven Smith, expected to be named as Test captain following Clarke’s retirement, is named skipper.
Current T20 captain Aaron Finch was not selected after fracturing his foot while playing for Yorkshire last month.
“The reality is Aaron isn’t fit for selection at this stage and he also hasn’t played as much cricket as we would have liked him to following a couple of serious injuries,” Marsh said.
“He will return to Yorkshire, fitness dependent, for a few games of four-day cricket at the end of the season as he prepares for the Australian summer.”
Leg-spinner Cameron Boyce has been included for selection for the T20 International game.
The Australian Test team has endured a tough tour in Britain so far, losing the Ashes series ahead of the fifth and final Test which begins at The Oval on August 20.
Australia will play a one-off ODI against Ireland in Belfast on 27 August and a T20 match against England on 31 August in Cardiff. They will then play five ODIs against England beginning 3 September.
Australia: Steve Smith (c), Ashton Agar, George Bailey, Joe Burns, Nathan Coulter-Nile, Patrick Cummins, Glenn Maxwell, Mitchell Marsh, James Pattinson, Mitchell Starc, Marcus Stoinis, Matthew Wade (wk), Shane Watson, David Warner, Cameron Boyce (T20 only).