David Warner, 28, will be the Test team's vice-captain.
"When Michael made his decision to retire last week it was a very straightforward decision for us to nominate Steve as his successor," chief national selector Rod Marsh said in a statement.
Read: Sarfraz to lead Pakistan A against England Lions
"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."
Smith will also be Australia's T20 captain during their tour of the British Isles due to Aaron Finch's injury.
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