LA Opera's board of directors said in a statement Monday it was "consolidating the duties" of general director with Koelsch's current jobs.
Domingo resigned as general director, a job he held since 2003, saying his ability to continue at LA Opera was compromised by the accusations against him.
In reports published by The Associated Press, more than 20 women accused the legendary tenor of sexual harassment and inappropriate conduct. Domingo has denied any wrongdoing.
Koelsch has held various positions at LA Opera since 1997 and was appointed president and chief executive in 2012.
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