The boats - the Century IV and Century VII - were caught south of Merauke in Indonesia's Papua Province on December 7.
According to the Jakarta Post, the crews on both vessels were all Thai nationals, despite the boats flying the PNG flag. The vessels were carrying 63 tonnes of fish and shrimp.
Indonesian Navy spokesman Commodore Manahan Simorangkir said the ship owners were found guilty of offences in court and destroying the vessels would help discourage illegal fishing.
"The ships have gone through legal procedures at the court in Ambon and their owners were found guilty of stealing fish from Indonesian waters," he said.
"We must sink these ships so that other foreign ships will think twice before fishing illegally in our territory."
The policy of sinking foreign ships found illegally fishing in Indonesia's economic exclusive zones has been championed by President Joko Wododo, considering the annual loss to the nation through illegal fishing is estimated to be US$24.3 billion ($A30 billion).