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.
Burns proved he was "a very capable young batsman who has experience opening", said Marsh.
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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.