In its latest update on the El Nino Southern Oscillation (ENSO), the bureau says La Nina conditions are no longer present in either the Pacific Ocean or the atmosphere.
It said the 2011-2012 La Nina began last spring, and played a key role in prolonged wet conditions for eastern Australian throughout summer and into early autumn.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"South-east Australia recorded its wettest seven-day period in history, and the combined effect of two back-to-back La Nina events contributed to Australia's wettest two-year period on record," the bureau said.
The weather bureau's manager of climate prediction services, Dr Andrew Watkins, said that while this La Nina may be over, we still need to be cautious.
"The oceans around Australia remain warmer than normal, and the tropical wet season is expected to remain active until the end of April, bringing with it the possibility of tropical cyclones and further heavy rain," Dr Watkins said.
He said the likelihood of a third successive La Nina remained low, with none of the models used by the bureau indicating a return.
