The attack, the first of its kind in Taiwan, targeted the First Commercial Bank's ATM network in July and saw money withdrawn from dozens of machines in three cities.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 the Taipei District Prosecutors Office.
Police said last month they believed the heist was carried out by an international crime ring.
The three were charged with fraud and offences related to computer security, the statement added.
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It said 19 other suspects, including one Australian, one French national and an unknown number of eastern Europeans, had been added to the government's wanted list after they fled Taiwan following the heist.
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.
Last month, Thai police said they believed a similar heist - where a gang of foreign criminals stole at least $346,000 by hacking a Thai bank's ATM network - was believed linked to the one in Taiwan.