Papaconstantinou, 53, received a one-year suspended prison sentence.
He had faced a possible sentence of 10 years to life imprisonment over the felony charges after being accused of removing the names of three of his relatives from a list of Greeks with accounts at HSBC bank in Geneva.
The former minister had vehemently denied the charges against him. In a majority ruling, the panel of 13 judges found him guilty of doctoring a document but reduced the count to a misdemeanour.
"After a very thorough and detailed procedure ... was clearly demonstrated in court was that Mr. Papaconstantinou had no intention of harming the Greek state and of course did not harm it," his lawyer Vassilis Dimakopoulos told reporters after the trial ended.
"This lack of damage and any self-interest confirms my client's reputation, which the defence was proud to uphold."
The bank account list became known as the Lagarde List, named after Christine Lagarde who was France's finance minister at the time and who sent the information to Papaconstantinou in 2010. It was an extract of a list of HSBC Geneva account holders leaked by former bank employee Herve Falciani.
Successive Greek governments have come under criticism for not investigating all the names on the list to determine whether those on it had evaded taxes.
Papaconstantinou served as finance minister from late 2009 to mid-2011 and was the minister who negotiated Greece's original international bailout, under which the country in May 2010 began receiving rescue loans from other eurozone nations and the International Monetary Fund in return for pushing through reforms to overhaul its economy.
The case was heard by a special court set up to handle trials against politicians. Of the 13 judges, eight called for a guilty verdict on the document- tampering charge, with three of them calling for a felony count and the other five a misdemeanour.
The remaining five judges had called for an acquittal.
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