The digital revolution that flummoxed the music, movie and publishing industries has given rise to a surprising winner: the audiobook.

Audiobooks are the fastest-growing format in the book business today. Sales in the U.S. and Canada jumped 21% in 2015 from the previous year, according to the Audio Publishers Association. The format fits neatly in the sweet spot of changing technology and changing behavior. Carrying around a pocket-size entertainment center stuffed with games, news, music, videos and books has conditioned...