With regular skipper Clarke expected to miss the rest of the four-match Test series due to injury, Smith was handed the job after Australia’s first Test victory in Adelaide on Saturday.
Smith smashed 162 not out in the first innings and was 52 not out in the second.
CA looked to the long term and officially first appointed Smith vice-captain on Monday and then named him to lead the Test side.
Veteran wicket-keeper Brad Haddin who led Australia on the final day of the Adelaide game will serve as deputy in Brisbane.
National selector Rod Marsh said: “These are difficult circumstances given Michael’s injury and the fact that we don’t know how long he will be out of the game.
“What we do know is that it won’t be an overnight fix so after a lot of thought we have taken the opportunity to appoint an emerging young leader as captain until such time as Michael regains fitness and returns to the side.
“We congratulate Steve on the wonderful honour of leading his country. On Wednesday he will become Australia’s 45th Test captain and at the age of 25 will become one of our youngest leaders.
“He is an exceptional young man who is highly regarded by the National Selection Panel not only for his fine performances with the bat but also his maturity and clear leadership potential.”
Marsh paid tribute to Haddin, 37, saying he had “done an exceptional job as vice-captain since assuming the role last year and will provide strong support to Steve just as he has done for Michael.
“There was a strong argument for Brad to assume the captaincy until Michael returns, but given we don’t know how long that will be, we felt the time was right to take a longer-term view and give a young player this chance.”
CA chairman Wally Edwards said: “Steve is an impressive young leader who deserves high praise for his temperament and on-field performances to date.”
Clarke’s immediate playing future is up in the air and he is now focusing on getting fit for the World Cup, which starts in Australia and New Zealand on February 14.
He was disconsolate following Australia’s 48-run first Adelaide Test win over India after being forced off with a torn right hamstring.
If Clarke returns he will do so as captain, with Smith serving as deputy, CA said.