Opening batsman David Warner will be Smith's deputy in the test and one-day international formats, Cricket Australia said in a statement.
Clarke announced his decision to quit international cricket after England won the fourth test at Trent Bridge last week to regain the Ashes.
The 26-year-old Smith was expected to take the role having previously led the team when he replaced the injured Clarke as captain for three tests during the home series against India.
National selector Rod Marsh said Australia had no doubt that Smith was the right man for the job.
"We have had a clear succession plan in place for the captaincy with Steve Smith gaining valuable experience leading the Australian test team while Michael Clarke was recovering from injury last season," Marsh said in the statement.
"When Michael made his decision to retire last week it was a very straight forward decision for us to nominate Steve as his successor.
"He has big shoes to fill but everything about him suggests he is the right man for the job. At 26, he is a fine young man with extraordinary talent, excellent leadership qualities and a terrific temperament.
"He is highly regarded by the selectors and we congratulate him on being appointed to the role on an ongoing basis. He should be incredibly proud."
Smith has clearly been Australia's best batsman in the last year but his team is certain to have a very different complexion when they embark on a two-test tour of Bangladesh in October.
Wicketkeeper Brad Haddin, Chris Rogers and Shane Watson are all expected to have played their last tests during their calamitous trip to England, while paceman Ryan Harris retired before the first Ashes test after suffering another knee injury.
Besides Smith, the diminutive Warner is expected to carry most of the burden of Australia's batting.
Nicknamed 'Bull' and one of the cleanest hitters in the game, Warner, when on song, can take a game away from opponents but also relishes a verbal battle out in the middle and his sledging has drawn multiple code of conduct violations in the past.
However, Marsh felt the extra responsibility would help the left-handed batsman.
"We have reached a point in time where we've had to look at our leadership positions again with an eye to the future," Marsh said.
"David has matured and developed into an important senior figure in the Australian team. He has come a long way.
"We believe that he will respond well to the added responsibility of leadership."
The fifth Ashes test starts on Thursday at The Oval, London.
(Writing by Sudipto Ganguly in Mumbai; editing by Patrick Johnston)
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