David Mitchell was wordless for the first five years of his life. It's an irony of an autobiographical detail which critics and interviews can't resist, that the writer loved for his abundance of stories-within-stories, began as a child unable to say anything at all before growing into a teenager afflicted with a stammer. Now, six books into his career and regarded by many as his generation's greatest writer, the twice Booker-shortlisted 45-year-old is applying his prodigious eloquence to what he calls the most "straitjacketed" form: Twitter.

The Right Sort is a short story being published in flurries of tweets sent from an account (@david_mitchell) which the author set up specifically for this purpose. Mitchell has explained that his choice of medium fits his protagonist, a young boy who steals his mum's Valium "because it reduces the bruising hurly-burly of the world into orderly, bite-sized 'pulses'". So the boy is essentially thinking and experiencing in tweets."

There's this, for example, tweeted last Monday: "The pill's just kicking in now. Valium breaks down the world into bite-sized sentences. Like this one. All lined up. Munch-munch."

It's just a tweet, but it also seems like confirmation of the specific talent that New Yorker critic James Wood praised in a lengthy panegyric in 2010. Namely that "he may be self-conscious, but he is not knowing, in the familiar, fatal, contemporary way; his naturalness as a storyteller has to do not only with his vitality but also with a kind of warmth, a charming earnestness".

Wood's review ran under the title: "What can't the novelist David Mitchell do?" Clearly, "prove that Twitter fiction can be art, not gimmickry" is just another one for the "can- do" list.

His tweeted story is an intriguing project in its own right, but it's also an appetite whetter for the main dish, his sixth novel, due in several weeks' time. The Bone Clocks begins in the Thatcherite Britain of 1984 in the distinctive voice of Holly Sykes, a mouthy teenage runaway who also happens to be a kind of human transceiver of psychic phenomena. As a child she experienced a constant heard and unseen chorus which she called "the Radio People" and now, as a 15-year-old on the run from a definitive row with her mother, she encounters an inscrutable old woman who gives her a cup of green tea in exchange for an unspecified "asylum".

This mystical transaction sets in motion a story in six instalments, each one for a decade of Holly's life. By the time we reach the last, in 2042, she's no longer the girl lobbing Talking Heads vinyl off the Kent coast, but a wise old woman living by the sea in Ireland in an oil-exhausted future.

Ireland is where Mitchell himself now lives with his wife and two children, but he was born in Ainsdale, near Southport to artist parents and grew up in Malvern, Worcestershire. With traditional – if not obligatory – British self-deprecation, he's downplayed the artsiness of his upbringing. Speaking to the Paris Review in 2010 he said: "When I talk about my artist parents people imagine a bohemian environment [...] but we were as white, straight, and middle-class as the next family on our white, straight, middle-class housing estate."

It was no surprise to his parents that their bookish son went on to study comparative literature. At the University of Kent he was taught by Jan Montefiore, who also employed him as a babysitter for her young sons. Mitchell wrote bedtime stories for them which featured, for example, an eagle that spoke in Chaucerian rhyming couplets. When she saw these, Montefiore was so charmed and dazzled that she told Mitchell: "One of those days I'm going to boast about having had you as a student".

Ten years later, Mitchell published Ghostwritten and Montefiore got her chance: the book was widely acclaimed as the best debut novel of the year, if not the decade.

In truth, it wasn't his first. After graduating, he taught English as a foreign language in various countries around the world and it was while in Hiroshima that he wrote The Old Moon, a sprawling book of 365 chapters dense with characters and subplots.

It was roundly rejected by agents, among them Mike Shaw, who deemed the manuscript "a mess" – "out of control and over the top". Sensing talent however, he asked Mitchell to send him whatever he wrote next. When Shaw read Ghostwritten, he was astounded at how far he had come.

Since then, Mitchell's reputation has grown with each book. His second novel, 2001's number9dream, was a coming-of-age story set in Japan, then, in 2004, he published Cloud Atlas, a collection of "nested" stories in which each tale is read by the main character in the tale that follows. The novel's scope is enormous, moving from the remote South Pacific of the 19th century to a dystopic future Korea.

It's here that the novel's one ostensibly non-human character – a genetically engineered clone called Sonmi~451 – articulates the novel's central human truth: "Our lives are not our own. From womb to tomb, we are bound to others. Past and present. And by each crime and every kindness, we birth our future."

After this came 2006's Black Swan Green, which, with a 13-year-old Worcestershire lad who stammers as its protagonist, is Mitchell's most autobiographical work. It won him a fresh round of literary laurels, but perhaps the accolade that pleased him most was making it on to course syllabuses for speech therapists in the UK.

Then, in 2012, Mitchell experienced an even more unexpected honour when Cloud Atlas was adapted for film. As he put it: "This eight-year-old Russian doll of a novel by some British bloke nobody's ever heard of," became a $100m movie. Directed by the Wachowski brothers and Tom Tykwer, the film was stuffed with stars – Halle Berry, Tom Hanks, Susan Sarandon, Ben Wishaw, Jim Broadbent, Hugh Grant – but suffered from being stuffed in every other way too.

One critic complained: "It plays like a gargantuan trailer for a movie still to be made." And that voice wasn't alone in finding a movie thick with bombast and dazzle and thinner on emotional nuance.

Mitchell, ever sanguine, wrote a defence of the movie in the Wall Street Journal: "Adaptation is a form of translation, and all acts of translation have to deal with untranslatable spots." Later, in an interview with the Guardian, he said: "If the film doesn't work, it doesn't hurt the book. If it does work, it helps the book."

In fact, sales of the book rocketed. Suddenly, this mild-mannered Englishman found his dense, complicated epic of a postmodern novel competing with Fifty Shades of Grey on the New York Times bestseller list – a place that Mitchell, for all his wildly imaginative, geographically restless adventurousness, probably never expected to find himself.

In a review of Hari Kunzru's Gods Without Men, Douglas Coupland sought to coin a new literary genre. Name-checking Cloud Atlas, he wrote: "Translit novels cross history without being historical; they span geography without changing psychic place. Translit collapses time and space as it seeks to generate narrative traction in the reader's mind. It inserts the contemporary reader into other locations and times, while leaving no doubt that its viewpoint is relentlessly modern and speaks entirely of our extreme present."

Kunzru, who, like Mitchell, was a Granta best young novelist in 2003, is both a friend and fan. He tells me: "His signature is a kind of ineffable sense of the cosmic interconnectedness of everything. I'm not sure what that amounts to – he seems to flirt with notions of reincarnation and a kind of transcendental consciousness – but it allows him to flow freely into imaginary futures and pasts, which is highly pleasurable for the reader. It's a hopeful position too – I think that hopefulness partly accounts for his popularity, along with a kind of gentleness, a basic ethical decency. Readers can tell he's a nice guy on the page."

Virtuosity and modesty do not, historically, go hand-in-hand, but in Mitchell's case they seem to come from the same place, namely a perennial boyish excitement about the world. One young character in The Bone Clocks, a teenage boy called Brubeck, confides in Holly: "Sometimes I want to be everywhere, all at once, so badly I could just..." and he mimes "a bomb going off in his rib cage".

It's hard to resist reading that as pure ventriloquism from an author whose fiction continues that magic trick of being everywhere, all at once.