Announcement comes on same day Smith and Bancroft apologised on television while Warner issued a statement on social media.
Darren Lehmann steps down as Australia coach in light of ball-tampering scandal
Australia cricket coach Darren Lehmann said on Thursday he would quit after the final match of the scandal-tainted Test series in South Africa after the team's former captain Steve Smith broke down in tears and accepted complete responsibility for the ball-tampering incident.
Smith was deeply emotional as the man at the centre of a storm that has rocked world cricket arrived back in Sydney from Johannesburg after being banned for a year from the sport.
"I take full responsibility, I made a serious error of judgement and I understand the consequences. It was a failure of leadership," Smith said, choking back tears as he was comforted by his father Peter.
"I know I will regret this for the rest of my life. I am absolutely gutted. Cricket is my life and I hope it can be again. I'm sorry. I'm absolutely devastated."
Within hours, Lehmann said he was standing down despite Cricket Australia saying he had had no knowledge of the plot to alter the condition of the ball in the third Test in Cape Town.
"This will be my last Test as head coach of the Australian cricket team," Lehmann, who also had tears in his eyes, said. "Saying goodbye to the players was the toughest thing I have ever had to do."
Lehmann said "the feeling is that Australian cricket needs to move forward and this is the right thing to do".
Roughing up one side of the ball would have given Australian bowlers an advantage by producing more swing.
Cricket Australia have banned Smith and vice-captain David Warner from all international and domestic cricket for a year while Bancroft was exiled for nine months.
Smith's fall from grace has been dramatic, and fast. He was jeered as he made his way through Johannesburg airport on Wednesday surrounded by police and media with concerns over his mental state in the current heated climate.
Warner, a divisive figure who was charged with developing the plot and instructing Bancroft to carry it out, also broke his silence to say sorry and admitted his actions had been "a stain on the game".
"Mistakes have been made which have damaged cricket," he told his 1.6 million Instagram followers. "I apologise for my part and take responsibility for it."
An emotional Bancroft said he was ashamed when he arrived back in Perth.
"All I can do in the short term is ask for forgiveness," he said, while denying he had ever tampered with a ball before, in comments echoed by Smith. "This is the first time I have seen this happen and it will never be happening again."
Smith and Bancroft will not be considered for team leadership positions until a minimum of 12 months after the end of their suspensions, and Warner will never lead again.
Wicketkeeper Tim Paine will take over the Australian captaincy for the fourth and final Test starting in Johannesburg on Friday.
The International Cricket Council said it will review its punishment for ball-tampering in light of the Australia scandal, and warned the game is in danger unless decisive action is taken.
ICC chief executive David Richardson, a former South African wicketkeeper, said the affair had been an "eye-opener".