According to the Police Central e-Crime Unit (PCeU), a number of major financial institutions in the UK are thought to have suffered losses following the hack.
The authorities believe that a variety of malicious codes such as the Trojan Zeus were utilised by the criminals to steal log-in details from customers.
These codes were then used to make fraudulent transfers, which are thought to have cost British firms as much as Â£6 million over a three-month period.
Terry Wilson, detective chief inspector from the PCeU, said: "We've worked closely with UK banks through our Virtual Taskforce approach to gather information and evidence which has resulted in today's arrests.
"We believe we have disrupted a highly organised criminal network, which has used sophisticated methods to siphon large amounts of cash from many innocent peoples' accounts, causing immense personal anxiety and significant financial harm - which of course banks have had to repay at considerable cost to the economy.â
The police unit arrested 15 men and four women as part of the investigation.
By Jim Ottewill