Tate was part of the team that won the K4 gold medal at the London Games and his out-of-competition samples, provided in Hungary on July 21-22 last year, tested positive for the steroid stanozolol.
The 33-year-old had appealed to the Court of Arbitration for Sport, which handed down a two-year ban, the Australian Olympic Committee said in a statement.
Smith's ban has been backdated to the day he was provisionally suspended and he will be ineligible to compete until Sept. 8, 2016.
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(Reporting by Sudipto Ganguly in Mumbai; editing by Peter Rutherford)
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