Bancroft returned to action in December after his suspension for his part in the Australian team's plan to change the condition of the ball during a test match in South Africa last year.
Australia captain Steve Smith and his deputy David Warner were both handed one-year bans for their roles in the incident.
Bancroft replaced as Durham captain former England all-rounder Paul Collingwood who retired at the end of last season.
"He's proven since returning to first-class cricket over the last few months that he has the mental toughness, skill and attitude to excel at the highest level and I'm sure he will relish the challenge we have at Durham this season," Durham's Lead High Performance Coach James Franklin told the club's website on Thursday.
"We're delighted to have Cameron with us for the season and we're confident he has the attributes to lead this exciting young Durham dressing-room."
The 26-year-old returned to action in the Big Bash League and has played four-day cricket for Western Australia.
Bancroft was caught on camera trying to tamper with the ball using sandpaper during Australia's test against South Africa in Cape Town last March. He admitted he lied in a subsequent news conference, saying he used sticky tape covered in dirt to change the ball's condition.
Smith later admitted the plan to use sandpaper had been hatched by the team's leadership group and in a later interview Bancroft, a relative newcomer to the side, said he had carried out the instruction to "fit in".
Bancroft, who has eight test caps, could be named in Australia's squad for the Ashes series in England this year.
(Reporting by Martyn Herman, editing by Ed Osmond)
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