“The drama is over,” Mr. Bachler said in a telephone interview.

Mr. Bachler said that he planned to reinvent the festival, which was originally conceived as a vehicle for the Berlin Philharmonic, and more recently served as one for the Staatskapelle. His idea is to bring different leading orchestras and conductors each year to explore repertoire in which they specialize. Mr. Bachler also plans to reconfigure the 10-day event to make it more immersive, with offerings from morning until late at night.

In his letter to festival officials, Mr. Thielemann, who is also the music director of the Bayreuth Wagner Festival, wrote that he had hoped to conduct Wagner’s “Lohengrin” in Salzburg in 2022, and Strauss’s “Elektra” there in 2023. The festival officials split the difference, announcing that Mr. Thielemann would conduct “Lohengrin” as his farewell in 2022. (A spokeswoman for the Staatskapelle said that neither the orchestra nor Mr. Thielemann had any comment.)

Mr. Bachler will take over the festival’s business operations in 2020 — when he will overlap with Mr. Thielemann — and become artistic director in 2022. He has a close rapport with the conductor Kirill Petrenko, the music director of the Bavarian State Opera, who became chief conductor of the Berlin Philharmonic last month. He said that he hoped to lure the Berliners — who have played at Baden-Baden’s Easter Festival since leaving Salzburg — back, as one of the rotating guest orchestras he hopes to attract.

“That,’’ Mr. Bachler said, “is my big wish.”

Sept. 17, 2019