The arrests were made after searches of the men’s homes in Penrith, New South Wales, and Scarborough, a suburb of Perth in Western Australia.
Australian police said the data stored on several hard drives and other computer equipment seized is expected to take several months to analyse, reported the Guardian.
It is believed the two men knew each other online and targeted organisations including a large internet service provider and web servers hosting Australian and Indonesian government websites.
The 40-year-old Scarborough man was charged with the unauthorised modification of Melbourne IT internet firm’s network in Brisbane and Indonesian government web servers to cause impairment.
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He has appeared in Perth magistrates court, and released on bail on a number conditions, including not using the internet for any purposes other than banking, employment or legal advice, reports ABC News.
The 18-year-old Penrith man was charged with the unauthorised modification of data to NetSpeed ISP in Canberra and restricted data of the ACT Long Service Leave Board in Canberra to cause impairment.
He is due to appear in Sydney central local court on Thursday.
The attacks, which date back to 2012, resulted in theft of personal data, defacement of websites and distributed denial of service attacks to knock a number of websites offline.
In November 2013, Indonesian hacktivists claimed to have hacked more than 100 Australian websites in response to reports that the Australian embassy in Jakarta was used for spying.
The hackers, who claim to have links to Anonymous, defaced dozens of websites belonging to Australian businesses.
The defendants admitted taking part in Operation Payback, in December 2010, that targeted payment firms such as Paypal, Mastercard and Visa, after those companies stopped processing donations to Wikileaks.