Munich prosecutors said they had not found proof of bribery to secure the two-billion-euro contract for the sale of 18 Eurofighters to the Austrians.
But they concluded that Airbus management failed in its supervisory duty to by allowing employees to make multi-million-euro payments for "unclear purposes".
Although the statement says the German probe "has been terminated", the company faces a lawsuit by the Austrian government seeking 1.1 billion euros in damages.
It accuses the company, previously known as EADS, of misleading it, overcharging to make up for kickbacks and other expenses.
Current Airbus chief Tom Enders was head of the EADS defence arm at the time.
He will not be seeking reappointment when his current term ends in April 2019, the company announced in December.
Britain and France are also investigating Airbus over corruption allegations relating to its UK-based civil-aviation arm.
The company, which itself brought the case to the authorities' attention, has warned that the investigations should hurt its profits and business prospects.