Australians Banned For Ball Tampering
Smith, 28, and Bancroft, 25, have also been suspended from captaining Australia for at least the next two years.
Warner, 31, will not be considered for "any team leadership positions in the future", Cricket Australia said.
Cricket Australia had already concluded that coach Darren Lehmann was not involved in the controversy and he will remain in his post.
The body's chief executive James Sutherland said the three players were "sad, disappointed and remorseful".
He added: "This has caused damage to the game as a whole and certainly to Cricket Australia. It has compromised the fans' faith in cricket and it's our responsibility to reinstate that confidence.
"It appears to be an isolated incident but if there are other allegations we will take them further. There was some courage in owning up but there was an element of untruth and that's something we took into consideration."
Smith, Warner and Bancroft are banned from international and Australian domestic cricket. They will also serve 100 hours of "voluntary service in community cricket" and can appeal against the suspension.
Cricket Australia said the players would be "permitted to play [Australian] club cricket and will be encouraged to do so".
They also remain eligible for competition outside of Australia, but earlier on Wednesday Smith and Warner were also banned from this season's Indian Premier League.