Bancroft had said he used tape and dirt, though Cricket Australia said on Wednesday that it was sandpaper.
The severe punishments were confirmed by CA on Wednesday.
CA chairman David Peever said: “The CA board understands and shares the anger of fans and the broader Australian community about these events.
“They go to the integrity and reputation of Australian Cricket and Australian sport and the penalties must reflect that.
“These are significant penalties for professional players and the board does not impose them lightly. It is hoped that following a period of suspension, the players will be able to return to playing the game they love and eventually rebuild their careers.”
Smith and Bancroft gave a press conference after the third day’s play, on Saturday, where they admitted a premeditated attempt to tamper with the ball.
CA chief executive James Sutherland announced on Tuesday that the pair, and vice-captain Warner, would be sent home but the investigation concluded that no-one else, including coach Darren Lehmann, was involved.
Matt Renshaw, Glenn Maxwell and Joe Burns have been called up as replacements ahead of the fourth and final Test in Johannesburg.
Tim Paine, who took over from Smith as captain mid-match in Cape Town as the furore began to unfold, was officially appointed as captain of the Test team on Tuesday.
Smith and Warner have also been banned from taking part in this year’s Indian Premier League.
The duo had already stepped down from their roles as captain of their franchises, Smith at Rajasthan Royals and Warner at Sunrisers Hyderabad.
A statement from the Board of Control for Cricket in India read: “The Hon’ble Supreme Court of India appointed Committee of Administrators (CoA) on Wednesday took cognizance of the developments in the ball tampering incident involving Cricket Australia contracted cricketers – Mr Steve Smith, Mr David Warner and Mr Cameron Bancroft.
“The CoA, in consultation with BCCI acting president Mr CK Khanna, IPL chairman Mr Rajeev Shukla and BCCI acting hon. secretary Mr Amitabh Choudhary, has decided to ban Mr Smith and Mr Warner with immediate effect from participation in IPL 2018.”
It is a heavy price to pay for the players, especially Smith, the world’s number one ranked Test batsman who will now lose a year of his career.
Warner has emerged as the apparent ringleader, with CA charging him with “development of a plan to attempt to artificially alter the condition of the ball”.
The 31-year-old will not be considered for a team leadership position in the future, CA added, while Smith and Bancroft will not be considered for such roles until 12 months after their bans end.
Smith, 28, was charged with “knowledge of a potential plan to attempt to artificially alter the condition of the ball”.
Bancroft, 25, playing in only his eighth Test, was charged with “knowledge of the existence of, and being party to, the plan to attempt to artificially alter the condition of the ball using sandpaper”, and “carrying out instructions to attempt to artificially alter the condition of the ball”.
All three players will be permitted to play club cricket, and will be encouraged to do so, to maintain links with the cricket community.
In addition, all three players will be required to undertake 100 hours of voluntary service in community cricket.
Meanwhile, a review into the culture of the Australian cricket team, brought into sharp focus in the wake of the scandal, will be published in due course.
Sutherland said: “The sanctions we have announced are significant for the individuals involved. That is why the process has had to be thorough to ensure that all relevant issues have been examined.
“I am satisfied that the sanctions in this case properly reflect a balance between the need to protect the integrity and reputation of the game and the need to maintain the possibility of redemption for the individuals involved, all of whom have learned difficult lessons through these events.
“As indicated, Cricket Australia will provide more details of an independent review into the conduct and culture of our Australian men’s team in due course.”