The attack, the first of its kind in Taiwan, targeted the First Commercial Bank's ATM network in July and saw money withdrawn from dozens of machines in three cities.
The suspects had uncovered a security loophole in a server at the bank's London branch office and used it to plant the malware, according to Taiwanese authorities.
Latvian Andrejs Peregudovs, together with Mihail Colibaba from Romania and Niklae Penkov from Moldova, were convicted of causing damage to the public by breaching computer security, said the Taipei district court.
Prosecutors had sought 12-year jail terms, saying their multiple actions had "seriously disrupted financial order and caused public panic".
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But court spokesman Liao Chien-yu said the judges had considered the illegal bank withdrawals as one case, which carries a maximum five-year sentence.
Prosecutors have said it was the first case of a multinational crime ring hacking into a bank's computer system to plant malware.
Thai police said a gang of foreign criminals stole millions of baht by hacking a local bank's ATM network in a theft last year believed to be linked to the one in Taiwan.
Surveillance images released by the bank showed masked robbers working in two-man teams targeting 41 ATMs in three cities from July 9-11. Within five to 10 minutes, the thieves were seen walking away with bags full of stolen cash.
Police arrested the trio in Taipei and northeastern Yilan county several days after the heist and recovered most of the stolen money.