Shane Watson was named as Clarke`s deputy, while Cameron White would continue as the Twenty20 skipper.
The 29-year-old batsman, widely tipped to lead the team, will immediately take charges.
Ricky Ponting had yesterday stepped down from the captaincy after the former world champions crashed out of the World Cup after the quarter-final defeat against India.
Ponting was also named in the squad which will leave for the Bangladesh tour.
"First of all I can say what an honour it is to be named captain and also a huge surprise to see Ricky stand down," Clarke said at a press conference in Sydney.
"I was very much unaware of where he was at and didn`t know he was going to stand down. It was a huge surprise to me.
"I know Ricky will allow me to do my job to the best of my ability," he added. "We want to be the best team in all forms and that is going to take time."
Clarke made his debut for the Australian one-day team in January 2003 against England at Adelaide. He was later chosen to make his Test debut against India at Bangalore in October next year.