Last week, Australia lost the Ashes Test series 1-3 to England. After the 4th Test, Clarke said he will bid adieu to international cricket at the completion of the 5th and final Test at The Oval, from August 20 to 24.
"Steve Smith will be the next captain of the Australian Test team following Michael Clarke's retirement at the end of the fifth Ashes Test at The Oval. The appointment was recommended by CA's National Selection Panel and endorsed today at Cricket Australia's August board meeting," Cricket Australia (CA) said in a media release on Friday.
The 26-year-old Smith has already been made the captain of the ODI side while Aaron Finch is the T20I skipper for Australia. However, Smith will be leading the T20I team too as Finch recovers from injury, CA said.
"Directors have endorsed a recommendation for opening batsman Warner to serve as Smith's deputy in the Test and One-Day international teams," CA said.
The 28-year-old Warner will be the vice-captain in the upcoming series of ODIs in Ireland and the United Kingdom followed by Australia's Test series against Bangladesh in September and October.
National Selector Rod Marsh said the appointments had been made with an eye to the future.
"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," said Marsh who praised Smith's performance over the summer when he became Australia's 45th Test captain in Clarke's absence.
"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."
Marsh said Warner had been chosen to support Smith in the Test and one-day international area.
"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.
"He had valuable experience captaining the Sunrisers in the IPL earlier this year and we are confident he will provide strong support to Steve as his deputy.
"We believe that he will respond well to the added responsibility of leadership."
Commenting on the announcement, CA Chairman Wally Edwards said: "The Board discussed the recommendation put forward by the selectors. We have all seen Steve Smith's clear leadership potential and believe he can perform an excellent job for Australian cricket over many years.
"We supported the recommendation to appoint David Warner as vice-captain, noting his role as a leading batsmen, his development and emergence as a leader within the team. We congratulate both men on their appointments," he said.