Finch will take over from George Bailey, who quit the leadership role yesterday (September 7) to concentrate on first-class cricket.
The 27-year-old Finch has played 18 T20Is for Australia and is a big-hitting right-handed batsman. He has a highest score of 156 in T20Is.
Finch said he was honoured to captain the Australian T20 side. "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.
"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 said.
Commenting on Finch's appointment, National Selector Rod Marsh said: "Aaron is the world's number-one ranked T20 International batsman and thoroughly deserves this opportunity."
"He has gained quality leadership experience through his role as captain of the Melbourne Renegades and the Pune Warriors. He also captained Australia A against the England Lions last year and excelled when given that chance," he added.
Marsh said Finch was the obvious choice for captaincy after Bailey's resignation.
"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."