Auckland-born Cooper took to social media on Thursday to share the news and thank his supporters.
"After five years, five attempts, 75 test matches and a lot of help from the community and many people behind the scenes, I can finally say I'm Australian," the playmaker posted on Twitter following his official ceremony.
"To my immigration officer Sarah Lolesio thank (you) for your efforts and countless hours of work. Grateful."
Now a dual citizen of Australia and New Zealand, Cooper cut a frustrated figure last July when he was denied for a fourth time for not meeting strict requirements while playing overseas in Japan.
But the Australian government changed eligibility rules late last year to ensure "distinguished applicants" could be eligible to become a citizen.
Cooper, 33, sat his test in Tokyo, where he continues to dazzle for the Hanazono Kintetsu Liners, in December.