David Warner, 28, will be the Test team's vice-captain.
Smith, who skippered Australia in Tests against India during the last home season when Clarke was sidelined with a hamstring injury, was the natural choice for the position, Cricket Australia said.
"When Michael made his decision to retire last week it was a very straightforward decision for us to nominate Steve as his successor," national selector Rod Marsh said in a statement.
"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, who was widely expected to replace Clarke and whose appointment was endorsed at Cricket Australia's August board meeting on Friday, will also be Australia's T20 captain during their tour of the British Isles, due to Aaron Finch's injury.
Australia's next Test series is against Bangladesh in September and October.
Marsh said Warner, who has attracted controversy over several incidents including punching England's Joe Root in 2013, had "matured and developed into an important senior figure in the Australian team".
"He has come a long way," Marsh said.
"He had valuable experience captaining the Sunrisers in the IPL (Indian Premier League) earlier this year and we are confident he will provide strong support to Steve as his deputy.
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