Paolo Cipriani, the former director general of the bank formally known as the Institute for Religious Works, and his deputy Massimo Tulli were convicted of failing to comply with anti-money laundering requirements.
The two were forced to resign in 2013 days after a senior Catholic cleric who held accounts at the bank was arrested in Italy for alleged corruption.
The cleric, Nunzio Scarano, was suspected of plotting to smuggle millions of euros into Italy. He was acquitted last year.
The investigation centred on a 2010 transfer of 23 million euros ($24 million at current rates) made from the Vatican bank to Italian lender Credito Artigiano in September 2010.
Three million euros were then sent on to Banca del Fucino and 20 million to JP Morgan Frankfurt. Both Cipriani and Tulli signed off on the transfers.
The court found that the two men neglected to provide sufficient information to JP Morgan, but they were cleared of irregularities in approving the 23 million euro transfer.
Prosecutors had sought a one-year prison term for Cipriani, and a ten-month term for Tulli.
The scandal led Vatican officials to pledge to clean up the bank, which handles the accounts of Vatican employees as well as clerics, religious congregations and diplomats affiliated with the Holy See.
The creation of a Financial Information Authority (AIF) in 2010 has led to the closure of about 5,000 accounts, and the agency said this month that it had frozen about two million euros in suspect funds last year as part of its corruption fight.
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