Bailey announced on Sunday he had stood down to concentrate on longer forms of the game with an eye to adding to his five test caps.
The rise of Finch, a short form specialist and an aggressive top order batsman, to the captaincy has been rapid, having made his international debut only three years ago in a T20 match against England in 2011.
"Aaron is the world's number-one ranked T20 international batsman and thoroughly deserves this opportunity," selector Rod Marsh said in a statement issued by CA.
"He has gained quality leadership experience through his role as captain of the Melbourne Renegades and the Pune Warriors," added Marsh of Finch's domestic T20 experience at home and in India.
"He also captained Australia A against the England Lions last year and excelled when given that chance.
"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.
"He has a task ahead of him. He is taking on a young side that is currently ranked fifth in the world. His first challenge will be building consistent performances as they head towards the ICC World Twenty20 in 2016."
Finch shattered the world record for the highest T20 international innings last year when he blasted 156 runs off 63 balls to guide Australia to victory over England in Southampton.
The 27-year-old also made his one-day international debut last year and has an average of 37.85 from his 28 matches, with a strike rate of 87.65.
"Having the honour to captain your country in any form of the game is something that all young cricketers dream about," said Finch. "It came as a big surprise but it was a very nice phone call to receive from Rod Marsh.
"I have been fortunate enough to play under some fantastic captains, including Michael Clarke and George Bailey and I have learnt a lot from them.
"It goes without saying that I will do my utmost in this role as we lead into the ICC World T20 in about eighteen months' time. It's going to be very exciting."
Finch will take first take the reins in a one-off T20I match against Pakistan in Dubai on Oct. 6, ahead of a test and one-day series against the same team.

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