Seven months after David Franklin abruptly resigned as director of the Cleveland Museum of Art, with museum officials later saying he had lied to them about his extramarital affair with an employee, the institution has named a high-profile successor from New York, signaling a new chapter in its 98-year history. He is William M. Griswold, who has led the Morgan Library & Museum for nearly seven years. Mr. Griswold, 53, who will start his new job in the fall, said he decided to leave New York because he relishes running a bigger institution, with one of the most encyclopedic collections in the country.

“All told, I’ve been at the Morgan for 13 years,” Mr. Griswold said, including his years as head of its drawings department, from 1995 to 2001, as well as his years as director, from 2008. “I’m ready for my last big challenge.” Mr. Griswold also ran the Minneapolis Institute of Arts for two years.