LONDON — Seeking to overcome one of its worst crises in decades, the British Broadcasting Corp. appointed Tony Hall, chief of the Royal Opera House, to be director general, replacing George Entwistle, who quit Nov. 10 amid scandal over the BBC’s reporting of sexual abuse.

The BBC quoted Chris Patten, head of the supervisory BBC Trust, as saying Hall, 61, a former news director at the BBC, was ‘‘the right person to lead the BBC out of its current crisis’’ and his experience in journalism would be ‘‘invaluable as the BBC looks to rebuild its reputation.’’ He takes the job in March.