Smith said he was not intimidated by the troubles in Boston, adding, “The B.S.O. is going through things that all organizations go through at certain times.” He said he would work to bring stability to the orchestra and to help it rethink its identity and mission.

“There are a lot of questions you have to ask,” he said. “Who do we want to be? What are those things that are absolutely essential? And where can we can continue to grow and expand and think differently about who we are and how we connect with audiences in our communities?”

Smith said that he would work to bring more racial, ethnic and gender diversity to the orchestra, which is less diverse than some of its peers. And he said that he was eager to keep Andris Nelsons, the music director in Boston since 2014, whose contract expires in 2025, calling him an “extraordinary musician.”

The challenges in Boston are familiar to Smith, who has spent 21 years at the Los Angeles Philharmonic, previously serving as its chief operating officer and vice president of artistic planning, developing a reputation for innovative programming and for forging ties to contemporary composers. He became chief executive in 2019 after the abrupt resignation of Simon Woods, who had been in the job for less than two years.

Like the Boston Symphony, the Philharmonic has been known for its artistic and financial success. Both institutions have benefited from having robust, and highly lucrative, outdoor summer offerings: the Hollywood Bowl in California, and Tanglewood in Massachusetts.

The loss of Smith will create a void in Los Angeles, where the orchestra is in the beginning stages of a search for a successor to Dudamel. Thomas L. Beckmen, the chair of the orchestra’s board, said in a statement that the Philharmonic was “confident our next leader will carry forward our values and vision and inspire the L.A. Phil to even greater heights.”