The 25-year-old, along with Australia captain Steve Smith and fellow batsman David Warner, were sanctioned by Cricket Australia after their involvement in a ploy to affect the ball in the third Test against South Africa in March.
Bancroft was banned for nine months while Smith and Warner are serving 12-month suspensions.
Durham announced on Friday morning that Bancroft would be available to play in all formats as their overseas player for next season.
The county's head coach Jon Lewis said: "Cameron provides us with a very talented overseas signing who can bulk up our batting line up and help us compete for silverware.
"Tom Latham has done a great job for us over the past two seasons but we anticipate Tom being unavailable due to the World Cup in 2019, therefore we were delighted to be able to bring Cameron in."
The press release announcing Bancroft's signing made no mention of the ball-tampering scandal.
The ball-tampering incident occurred on March 24, the third day of the third Test against the Proteas in Cape Town.
Bancroft was captured on camera applying a material to the rough side of the ball before placing it down the front of his trousers.
Bancroft initially said he used sticky tape, but Cricket Australia later confirmed it was a strip of sandpaper.
However, he was seen as the junior partner in the scandal, with Smith and Warner receiving longer bans for their part in it.
On March 25 Smith stood down as Australia captain after admitting his team deliberately tampered with the ball.
Bancroft, speaking about his decision to join Durham, said: "I am excited to join Durham for the 2019 county season. Having played at Emirates Riverside in 2017 I know what a great place it is to play cricket.
"With the Ashes and ODI World Cup both being played in the UK in 2019 it will be a huge summer of cricket. I am grateful for the opportunity and I can't wait to get over and make an impact with Durham."
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