The 27-year-old has taken on the responsibility after Bailey opted to step down from the role in order to focus on more first-class cricket.
"Aaron is the world's number-one ranked T20 International batsman and thoroughly deserves this opportunity," said national selector Rod Marsh.
"When George indicated that he was stepping down from the position, we thought Aaron was the obvious choice to succeed him. We know he will relish the opportunity to lead his country."
In October, Finch will captain the side in one T20 international against Pakistan in the United Arab Emirates prior to three one-day internationals and two Test matches between the two teams.
"Having the honour to captain your country in any form of the game is something that all young cricketers dream about. It came as a big surprise but it was a very nice phone call to receive from Rod Marsh," said Finch.
"I never imagined when captaining in the past that it would lead to national responsibilities. I've just set out to be the best player that I can and luckily an opportunity like this has come my way."
The batsman made his T20 international debut in 2011.