Bachler, who was born in Austria, will become the company's Intendant. or general manager, after his current contract with Vienna's Burgtheater expires in 2008.
He has also led Vienna's Festwochen and the city's Volksoper.
Both Jonas and music director Zubin Mehta are stepping down after the 2005-06 season. Kent Nagano will succeed Mehta in August 2006; he, managing director Roland Felber, director of artistic administration Ronald Adler, and public relations director Ulrike Hessler will administer the company jointly, advised by Jonas, until Bachler arrives.
"I am thrilled that Klaus Bachler is to become my successor as Intendant of this great company after I retire," Jonas said in a statement. "I have known and admired his work for many years and believe that this appointment can only be positive for an adventurous and secure artistic and financial future for this, the busiest and greatest opera company of the world. He is without doubt the right and most appropriate candidate for the task ahead."