For the first time in 60 years, the Metropolitan Museum of Art has reached beyond its own doors for a new leader, choosing a Vienna-born museum director who is conversant in the old masters, modern art and Minecraft to steer the venerable institution through the digital age.

The Met announced on Tuesday that Max Hollein, 48, currently the director and chief executive of the Fine Arts Museums of San Francisco and a veteran of Germany’s oldest art foundation, will become its 10th director this summer. He will take command of the Met at a time when museums are under increasing pressure to remain relevant, raise funds and attract new audiences.

“The Met is one of its kind,” Mr. Hollein said in an interview at the museum. “The museum has the opportunity to be not just an art destination,” Mr. Hollein added, but “a major provider of understanding and different narratives to a global audience.”

Unlike his recent predecessors Philippe de Montebello, who served for 31 years, and Thomas P. Campbell, who served for eight, Mr. Hollein did not ascend from the Met’s curatorial ranks. He was reportedly a runner-up when Mr. Campbell was chosen in 2008.