Speaking after arriving in Sydney from Johannesburg, he said: "I take full responsibility. I made a serious error of judgement and I understand the consequences. It was a failure of leadership. I'm sorry. I'm absolutely devastated."
Smith and David Warner were dismissed from their roles as captain and vice-captain and banned from international and domestic cricket for a year. Opening batsman Cameron Bancroft was suspended for nine months.
"I will do everything to make up for my mistake," Smith added. "If any good can come for this ... it can be a lesson for others. I hope I can be a force for change," he added.
"I know I will regret this for the rest of my life. I am absolutely gutted. Cricket is my life and hope it can be again. I'm sorry. I'm absolutely devastated."
Warner was charged by Cricket Australia with developing the plan to use sandpaper to alter the ball to their bowlers' advantage and instructing Bancroft to carry it out.
Smith, it has emerged, had effectively turned a blind eye to the plot. "For me, my weakness ... I have made a big mistake for allowing this to happen," he said. "This is the first time I have seen this happen and it will never be happening again.
"I don't blame anyone. I'm the captain of the Australian team and I take responsibility for the actions that happened."
Smith, whose batting exploits were starting to draw comparisons with the legendary Australian Donald Bradman, added: "I just want to say sorry for the pain I've brought to Australia, to the fans and the public."
Warner also broke his silence on Thursday. He apologised and accepted his role as a cheat.
Bancroft asked for forgiveness on his return to Perth. He said he was ashamed of himself.