The man was named in Australian media as Karm or Cam Gilespie.
He is believed to have been arrested at an airport in 2013 with 7.5kg (16 Ibs) of methamphetamine, also known as ice, in his luggage, the Sydney Morning Herald newspaper reports.
Australia's Department of Foreign Affairs and Trade said it was "deeply saddened to hear of the verdict".
"Australia opposes the death penalty, in all circumstances for all people. We support the universal abolition of the death penalty and are committed to pursuing this goal through all the avenues available to us," it said in a statement.