The conviction was quashed by the court but Matangi Tonga reported the former prime minister's appeal against conviction on one count of possessing gun ammunition, without a licence, failed.
In July 2015, the then prime minister had written a letter of support for two Chinese people trying to obtain passports.
But the Appeal Court found there was no evidence that Tu'ivakano intended to deceive.
Tu'ivakano had been found guilty on 9 March at the Nuku'alofa Supreme Court and given a suspended two-year sentence.
Six other charges, bribery and money laundering, were dropped.
Tu'ivakano keeps his hereditary noble title, estates and parliamentary seat despite the ammunition conviction.
The gun and ammunition charges related to items found during a police search of Tu'ivakano's property in March 2018.