“I feel like I’m always searching for someone…” Ever since the animation legend Hayao Miyazaki announced (perhaps prematurely) that 2013’s The Wind Rises was to be his final feature, fans have been searching for a successor to his artistic throne. Last week, Miyazaki revealed that 2019 may in fact see the completion of a full-length version of his short-film project, Boro the Caterpillar. But in the interim, an heir apparent has emerged in the shape of Makoto Shinkai, whose breathtaking body-swap romance Your Name has dominated the Japanese box office for months.

Revisiting themes of longing and separation that became his signature in films such as 5 Centimeters Per Second (2007) and The Garden of Words (2013), Shinkai’s fifth feature has confirmed the writer-director as a major talent, duly dubbed “the new Miyazaki”. Yet this rip-roaring, heartbreaking YA adventure is very much its own beast, as different from Miyazaki’s ageless Studio Ghibli animations as it is from live-action western romps such as Freaky Friday, The Hot Chick and It’s a Boy Girl Thing or, perhaps more pertinently, from Nobuhiko Ôbayashi’s 1982 Japanese hit, Tenkōsei.

Indeed, if you’re searching for a thematic touchstone, then the current Scandinavian release Girls Lost is probably a closer cousin, although Alexandra-Therese Keining’s intriguing teen-transfer fantasy seems drearily down to earth when compared with the wild flights of imagination that underpin Shinkai’s exuberant anime.

We open with a meteor shower, on “that day when the stars came falling, like a dream… a shared dream”. In the remote mountain town of Itomori, high-school girl Mitsuha longs for another, more exciting existence. “Please make me a handsome Tokyo boy in my next life!” she pleads, while performing her Shinto temple duties, which include the kuchikami ritual of making sake with spit and braiding kumihimo cords, representing the strange interweaving of time and space, of gods and men. One day, her wish comes true, as Mitsuha appears to awaken in Tokyo in the body of teenager Taki, a diffidently attractive young man who promptly starts to explore his “feminine side”.

Teen audiences in search of a “relatable” love story will find this every bit as accessible as Romeo + Juliet

Meanwhile in Itomori, Taki takes Mitsuha’s place, their spirits swapping back and forth at random, facilitating the need for smartphone messages to keep each other abreast of their oddly intimate adventures. For a while, the peculiar arrangement proves a boon to both, with boy and girl learning about each other’s lives and subtly altering their own accordingly. But something darker lurks in this dazzling tale, with the spectre of a rainbow-coloured sky threatening to fall upon the star-crossed couple who have become so close yet remain so distant.

Although its inspirations can be traced back to the late Heian-period tale Torikaebaya Monogatari, Your Name is a bristlingly modern affair with a J-pop soundtrack by teen favourites Radwimps and a mainstream cult sensibility that blends the fairytale charms of Hiromasa Yonebayashi’s 2014 adaptation of When Marnie Was There with the existential angst of Donnie Darko. The animation is thrilling, with the almost photo-realist views of Taki’s urban Tokyo life contrasting with the verdant hues of Mitsuha’s lakeside home.

Scenes of astral magic and natural disaster (an understandable preoccupation of Japanese cinema) lend a degree of spectacle that would put many live-action blockbusters to shame, while a hallucinogenic diversion into chalk pastel wonderment will transport even the most sceptical viewer to another realm.

Your Name by Makoto Shinkai. Photograph: Anime Ltd

Throughout, Shinkai juxtaposes male and female, town and country, science and superstition, past and present. But it’s in the twilight twinkling of kataware doki, when night and day meet and worlds old and new collide, that the real heart of this story lies. Like Chris Marker’s pioneering sci-fi La jetée (which inspired Terry Gilliam’s Twelve Monkeys), Your Name spirals elegantly towards a point where beginnings and ends become indistinguishable, but does so more in the manner of a melancholy coming-of-age comedy than an abstract arthouse experiment.

For all its thematic complexities, there is plenty to laugh about too, from a recurrent gag about Taki being caught fondling “his” breasts while in the throes of a body swap, to the gentle teasings of Taki’s co-worker Ms Okudera, who seems more attracted to the transposed Mitsuha than to any awkward boy. Teen audiences in search of a “relatable” love story will find this every bit as accessible as Baz Luhrmann’s Romeo + Juliet, while older viewers will delight in the way that archaic arts have become an integral part of 21st-century cinema.

Like the stories they tell, these moving pictures are a fusion of the ancient and modern. “Treasure the experience,” Mitsuha’s grandmother tells her sagely. “Dreams fade away after you wake up.” Not so this splendid movie, which will leave audiences in a heady reverie long after its mysterious light has faded from the screen.