"We are currently being investigated for alleged breaches of anti-bribery and anti-corruption laws," Enders wrote in a letter to employees seen by AFP.
"We are in this situation because we decided last year to disclose the issues we had ourselves uncovered to government authorities and investigation agencies," he said, adding: "This was the right course of action."
"This is going to be a long process and there are potentially serious consequences - including significant penalties to the company," Enders said.
An Airbus business unit in Paris reportedly built a network of shell companies linked to London-based Vector Aerospace, formerly the group's aircraft maintenance subsidiary.
Its system allowed the group to make "bribes to decision-makers in Austria" while Vienna was considering its purchase of Eurofighter military jets, German news magazine Der Spiegel reported Friday, culminating in a 15-aircraft deal worth about €1.7 billion ($2 billion).
Inquiries have also been opened in France and Britain, on suspicion of corruption in Airbus's UK-based civil aviation arm.
Without citing sources, Der Spiegel also reported that prosecutors were "preparing charges" against unidentified suspects over the Austria case.
"Internal investigators stumbled across more than 100 possibly corrupt payments in the three-digit millions," the magazine reported, citing anonymous sources.
But Hildegard Baeumler-Hoesl, a state prosecutor in Munich, told AFP earlier Friday that investigators had "little evidence so far of corruption".
Bavarian investigators have been looking into the Airbus since 2012, and the corruption probe over the sale of jets to Austria will "soon be over," she said.
An Airbus spokesperson told AFP that the Spiegel report was "not based on any declaration or disclosure by the public prosecutor."
Austrian authorities are also investigating Airbus after bringing charges in February, claiming the company paid out 183 million to €1.1 billion in under-the-table "commissions".
Austrian Defence Minister Hans Peter Doskozil accused Airbus and the Eurofighter consortium deliberately misleading Vienna about the purchase price, delivery times and technical equipment of the 18 Eurofighter jets.
Last month, Airbus denied the accusations, with a lawyer for the company calling them "factitious and legally groundless".
"As the process unfolds we are likely to face frequent media coverage," Enders said in his letter to employees, while also warning against "leaks and attempts by individuals with vested interests to discredit top management by spreading false allegations."
"In other words, prepare for turbulent and confusing times," he wrote.