The series also marks the returns of Josh Hazlewood and Pat Cummins to international cricket, with Hazlewood announced as one of two vice-captains alongside wicketkeeper Alex Carey. Mitchell Marsh has been rested for the series.
Finch has previously captained Australia in ODI cricket, standing in for two matches in New Zealand in early 2017. But in the wake of the ball-tampering scandal, Paine was announced as Test and ODI skipper and led Australia to a 5-0 series defeat in England earlier this year.
Finch, the T20 captain, looks set to lead Australia all the way through to the 2019 World Cup.
Chairman of selectors Trevor Hohns said Paine had been relieved of his duties "to focus purely on captaining the Test team, which includes preparing for next year's Ashes."
"As was the case when we announced the Test and T20 captains and vice-captains recently, the selection was based on their strong presentations which outlined their leadership credentials, the actions they have displayed on and off the field and the vision they have for Australian cricket," Hohns said.
"We expect Aaron, Josh and Alex to lead the side through a big Australian summer, where we'll meet South Africa and India, they'll also be driving our standards and values as we prepare our defence of the World Cup, which is only seven months away."
Hazlewood and Cummins have been preparing for the ODI series in the Futures League rather than the Sheffield Shield. They join a pace barrage which includes Mitchell Starc and Nathan Coulter-Nile. Andrew Tye has been squeezed out.
Shaun Marsh and Travis Head have both been named as expected with no concerns that their preparation for the India Test series will be compromised. Chris Lynn also returns to the ODI team after an outstanding JLT Cup for Queensland.
"Chris made it clear he wanted to be considered for the World Cup, and he backed it up with his performances for Queensland in the JLT Cup. He was the highest run scorer of the tournament and has been rewarded for his consistency," Hohns said.
Marcus Stoinis has been included after being omitted from the T20 squad to tour the UAE. Both Mitchell Marsh and Nathan Lyon have both been rested.
"We have made the decision to manage Mitch Marsh and Nathan Lyon carefully to ensure they are in the best condition possible to put their hand up for selection either later in the summer or for the World Cup next year," Hohns said.
Ashton Agar and Adam Zampa provide the spin options as they have in the UAE. Glenn Maxwell and D'Arcy Short have also retained their places.