The pen has been passed. The box-office success of animé director Makoto Shinkai’s new film, “Your Name,” marks a changing of Japan’s animation guard following the 2013 retirement of Academy Award-winning director Hayao Miyazaki.

“Your Name,” a time-traveling love story about two teenagers who switch bodies and lives, has grossed some $150 million in Japan since its Aug. 26 premiere. The film is the first major commercial hit for Mr. Shinkai and the fifth most successful animé movie in history, according to film-data provider Kogyo Tsushinsha.

Mr. Miyazaki’s “Spirited Away,” which won the Academy Award for Best Animated Feature in 2003, remains Japan’s highest-grossing film, at nearly $300 million.

Mr. Miyazaki, 75 years old, is Japan’s most popular and celebrated animé filmmaker. Over the course of his five-decade career, the director and his Studio Ghibli helped popularize the genre world-wide with hand-drawn images brimming with natural beauty and supernatural creatures.

When he announced his retirement from feature films three years ago, Mr. Miyazaki acknowledged a changing industry: “My time for long animated films has come to an end,” he said.