BERLIN — In this city of three major opera houses, a feted star of recent seasons has been off stage: Barrie Kosky, a self-described “gay Jewish kangaroo” from Australia who has staged everything from Rameau and Mozart to forgotten 1930s operettas and “West Side Story.”

Since becoming artistic director of the Komische Oper in 2012, Mr. Kosky, a 48-year-old native of Melbourne, has won a truly mixed audience for his often camp stagings. His house is 85 percent sold out, and both city fathers and picky critics appear delighted: At the end of Mr. Kosky’s first season, the Komische Oper was pronounced opera house of the year by 50 international critics, and in 2014 he was named best opera director.

“He takes Mozart as seriously as musicals, and Monteverdi as seriously as operetta,” said Wolfgang Prosinger, a columnist at Der Tagesspiegel. “And he has brought something of the glamour of Broadway to Berlin. That has helped change his audience: More and more young people are coming to the Komische Oper.”

Although young foreigners increasingly see this city as a must-visit capital of cool, Berlin remains a great repository of classical culture. The operas, Mr. Kosky noted in an interview, sell more than 800,000 tickets a year, mostly to the city’s roughly 3.5 million residents.