The Curious Case of Benjamin Button, David Fincher, 165 mins, 12A

David Fincher's new film is a curious case indeed, coming from the hitherto Stygian-minded director of such grim fare as Fight Club, Zodiac, and Se7en. Fincher has always been one of the wilder non-conformists in American commercial cinema, yet here he is making a film that, at first glance, is as capital-H Hollywood as they come: a lavish philosophical weepie that goes full out to make a grand statement about the human condition.

Mind you, when was the last time an American blockbuster entertained such ambitions? I can remember one occasion, for better or worse – Forrest Gump. The Curious Case of Benjamin Button does have at least two things in common with that intriguing but unlovable film. One is a twee title (in fairness, blame F Scott Fitzgerald, who wrote the story on which Fincher's film is based); the other is scriptwriter Eric Roth. Benjamin Button does contain its share of platitudinous Gumperies: "I think there and then she realised none of us is perfect for ever," goes one line of voice-over, and there and then I realised that not even a cinematic hard nut like Fincher always knows when to wield the blue pencil.

Even so, Fincher treats Roth's script with a visual bravura and narrative gusto far beyond the usual capacities of the Hollywood mainstream. Benjamin Button is a poetic, virtuoso feat, as eloquent and rapturous as CGI-era cinema gets.

The film thrives on Fitzgerald's simple but pregnant premise: its hero lives his life backwards. Benjamin (Brad Pitt) starts out a wizened old man in his eighties, then grows younger, becoming a teenager, a boy, an infant. Born in New Orleans on Armistice Day 1918, he is left by his horrified father (Jason Flemyng) on the porch of an old people's home run by Queenie (Taraji P Henson). She adopts this gnarly arthritic bundle, whose days seem numbered from birth. "He's on his way to the grave," a doctor diagnoses, and he's not wrong, though Benjamin thrives. Everyone's headed for the grave, after all: it's just that Benjamin has a clearly predetermined lifespan ahead of him, making his life more dramatically fated than most.

A geriatric infant, Benjamin eventually rises from his wheelchair, growing ever taller and less lined, until at last, a sprightly adolescent codger, he leaves home to see the world on a tugboat. He shares a tender romance with an Englishwoman in Murmansk (Tilda Swinton, doing her own rum, stately version of Celia Johnson crispness); then, the decades ticking by, he is reunited with Daisy (Cate Blanchett), whom he's known ever since she was young and he was old. The pair find happiness, but as he gets younger, she grows older, and although there's a precious, volatile interlude when they're both the same age – when they "meet in the middle" – they're fated to head in opposite directions thereafter, time travellers on different tracks.

The story is so strange and poignant that you might think the last thing it needed would be special effects. Yet the film's illusionism really does enhance the overall richness and mystery. Fincher's CGI team and effects makeup master Greg Cannom have created an extraordinary ancient-young Benjamin: a child-like homunculus with the physiognomy of a cranky greybeard but touched with big-eyed innocence and candour; Tiny Tim in the body of Methuselah. Although he's barely recognisable as Brad Pitt, you can see elements in little Benjamin's face of what Pitt could be in his dotage, and might have been at five, traces of both digitally distilled in this sweet-faced chimera. Inevitably, Benjamin becomes less bewitching as soon as he reaches an age to resemble Brad Pitt in a white wig. Meanwhile, Daisy ages: at first, a child with preternaturally blue eyes, then a young dancer, Cate Blanchett's digitally air-brushed features transplanted on to a ballerina's willowy body. Eventually, she's a soignée matron resembling Katharine Hepburn in her autumnal grandeur.

The moment at which the couple, both young adults, share a brief, evanescent "golden age" is the point at which, for some viewers, the film will look phoney and irredeemably kitsch – when an outrageously beautiful duo are seen under Florida sunsets, among the trappings of wealth and quasi-divine youth. But Fincher knows when he's dealing with cliché, and this sequence eloquently stages the quintessence of romance as impossible dream – bitter in its perfection because it is bound to evaporate under the force of time.

The couple's physical changes are used to unsettling and Freudian effect. Early on, little Daisy and little Benjamin hide under a table and are caught by her grandmother, who sees them not as two children, but as an innocent and a shameful old satyr. Later, a young woman relishing her newly acquired sophistication and sexuality, Daisy tries to seduce the father figure that Benjamin now seems. ("I can imagine dancing completely naked! Have you read D H Lawrence?")

Later again, their relationship takes on shades of incest, an older Daisy reunited with a younger Benjamin. Theirs is an encyclopaedic romance, taking in every conceivable colour of relationship that differing ages entail between lovers.

The film's picaresque sprawl can sometimes seem redundant, straining at fabulist scope. The film often says and shows too much. Late in the game, there's a laborious and overextended digression on chance, an idea explored far more mischievously in Paul Thomas Anderson's Magnolia.

But Benjamin Button is an extravagant film, and consequently a film of extravagant imperfections. Shot by Claudio Miranda, it dares sometimes to be too beautiful, too lavishly imagined. Over-stuffed with ideas, it nevertheless pursues its central idea with imagination and tenacity, and for all that it flirts with sentiment, the film has an irreducibly sober undertow that sets it far apart from big-screen orthodoxy: here is a Hollywood film that is wholly, committedly serious about death.

Benjamin Button resembles a gentler, more exuberant version of Günther Grass's The Tin Drum, about another exemplary boy-man travelling through history. It's also, if you like, a modern Pinocchio, for Benjamin too – at the start, an oddly puppet-like figure – eventually becomes a "real boy", and learns the lesson of mortality. What this isn't, by any means, is another Forrest Gump: if Benjamin Button in any way resembles a box of chocolates, rest assured they're as bitter as they are sweet, and very much made for adult tastes.