But he claimed at the time to have no ambitions to lead the orchestra, and the board went with an outsider: Mr. Woods, who had developed a reputation for innovation during his run as president of the Seattle Symphony. The staff he inherited included at least two people who had been discussed as contenders for his job. When he departed, he said in a statement that “after a great deal of reflection, I have concluded that my hopes and aspirations lie elsewhere.”

In a sign of how awkward the upheaval has been, and how quickly the change of leadership was put into place, Mr. Smith declined to be interviewed, which is rare for the incoming chief executive of a major orchestra. Sophie Jefferies, the orchestra’s director of public relations, said in an email that Mr. Smith was “not giving interviews at this juncture” and that he “would like time to set his vision for the organization and will talk later.”

It was not immediately clear what the appointment would mean for the Ojai Music Festival, about 90 minutes north of Los Angeles, where Mr. Smith recently began his tenure as artistic director. (His first edition of the festival is planned for June 2020.) Asked if running Ojai so near the Los Angeles Philharmonic and its summer home, the Hollywood Bowl, was seen as a conflict or complication, officials at the orchestra and the festival said that there would be no change at the festival.

After Mr. Woods stepped down, several prominent critics expressed support for Mr. Smith. In The Los Angeles Times Mark Swed described him as the “obvious” candidate. And several composers, including John Adams, praised his appointment on social media. “Sometimes,” Mr. Adams wrote in a post on Twitter, “things actually go right in the world, and today that happened in L.A. with Chad Smith being named to run the Philharmonic.”