The ABC said "multiple official sources" had confirmed the attack, and that it would cost millions of dollars to repair the damage.
ABC quoted unnamed officials blaming China for the alleged hack.
A spokeswoman for China`s foreign ministry denied that Beijing was responsible.
The BoM, which owns one of Australia`s largest supercomputers, said it would not comment on security matters and that its systems were fully operational.
It said in an statement that it "continues to provide reliable, on-going access to high quality weather, climate, water and oceans information".
The ABC said it had been told the attack was "massive", and quoted one official as saying it "could take years and cost hundreds of millions of dollars to fix".
There were no further details on which systems had been affected, whether information was taken, or on why China was seen as the likely culprit.
"We believe it is not responsible to make groundless accusations or speculation," a Chinese foreign ministry spokeswoman.
Among other services, the BoM provides climate information for commercial airlines and shipping, analyses national water supplies, gathers climate information and works closely with the defense department.
China has repeatedly been accused of using cyber-attacks to spy on foreign states and companies. The US has said the issue has put an "enormous strain" on their relationship.
Chinese officials have denied supporting cyber espionage and say China is itself a victim of hacking.
Australia Bureau of Meteorology hacked
02 December 2015
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Australia`s Bureau of Meteorology (BoM) has been the victim of a major hacking attack, the Australia Broadcasting Corporation has reported.
