Prosecutors had been seeking five-month jail sentences for Neil Bonner, 32, and Rebecca Prosser, 31, who were accused of having only tourist visas while attempting to make the film.
But the judge on the western island of Batam handed down a lesser sentence of two-and-a-half months, saying the defendants had admitted their guilt and apologised.
The pair, who have been detained since May, could now walk free after time spent in custody awaiting trial is taken into account.
"The defendants have been proven legally and convincingly guilty as foreigners who have violated staying permits in Indonesia," presiding judge Wahyu Prasetyo Wibowo told the packed Batam district court.
The pair arrived in Indonesia to shoot a documentary about piracy for production house Wall to Wall with funding from National Geographic, according to their indictment.
It added they had hired several Indonesians to act out a scene of a tanker being boarded by a group of pirates off Batam. The island is in the Malacca Strait, a major shipping lane.
Foreign journalists wanting to report in Indonesia must get a special visa. Foreign reporters detained in Indonesia for illegal reporting in the past have been deported immediately or given short prison terms.
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