Once upon a time, there was a magic kingdom. It was admired by all and brought laughter and joy to millions. But then the dark times came, an era when the magic kingdom lost its glister, metamorphosing into a land sunken in despair. Until, finally, a prodigal son returned, a former prince of the realm, and the man who could restore the magic kingdom to its former glory. The magic kingdom is, of course, Disney. The returning prince? John Lasseter, its new chief creative officer.

This 49-year-old animator, storyteller and business genius left the Mouse House in 1983 to join a young animation company called Pixar, where, as its creative architect, he helped to mastermind six consecutive box-office hits — Toy Story, A Bug’s Life, Toy Story 2, Monsters, Inc., Finding Nemo and The Incredibles. Now that Disney has finally acquired Pixar, in a £4 billion deal in January, Lasseter is once more firmly ensconced within the magic kingdom’s hallowed halls.

This is truly a fairytale ending for Lasseter and, in particular, for Disney. Visit the Science Museum between April and June and you’ll soon see why, for Pixar: 20 Years of Animation, which arrives after a successful stint at MOMA in New York, encapsulates the reasons for Pixar’s success. No other contemporary film studio has enjoyed a succession of six solid hits. In fact, Disney has to look as far back as 1994 for even one solid hit, The Lion King.

Indeed, the faltering animation giant made its first foray into 3-D animation only with this year’s anaemic Chicken Little, whereas 3-D animation is what Pixar is all about.

Meanwhile Pixar’s technologically savvy collection of creatives has redrawn the animation landscape, crafting films that display a rich sculptural reality, defined by immense spatial depth. And the exhibition, which features 250 concept drawings, sketches and paintings that trace the films’ evolution, from seed ideas to Oscar-winning masterpieces, reveals all Pixar’s secrets, laying them out in their kaleidoscopic glory.

At the heart of the exhibition stands an 8ft-long zoetrope, a computerised cinematic device that creates an optical illusion by setting static characters in motion. Via strobe lights and a revolving stage viewers will be treated to visions of Woody, from Toy Story, charging around on his horse while aliens dodge its hooves, Wheezy the penguin riding a seesaw, and Buzz revolving on a coloured ball.

But the exhibition reveals much more besides, guiding viewers through the development of character and narrative, the two foundation stones upon which the company’s success has been built. For all their pixel-related potency, Pixar movies are perfect paradigms of the storyteller’s art.

For a study in character evolution look no further than the marvellous images of Sullivan, who starts out as something rather terrifying before finally emerging as the blue-furred, cuddly creature in Monsters, Inc. The artist Pete Docter has Sulley and Mike sketched out in marker pen, with an almost calligraphic swish of simple lines, while Nicolas Marlet imagines him as a gelatinous blob studded with tiny eyes. In a fascinating mixed media piece by Tia W. Kratter we see the development of his fur pattern, while Dominique R. Louis presents him with collar, tie and an extra leg.

And Pixar has remained true to the primary tenets of animation, placing the pencil, as much as the computer, at the centre of the artist’s toolbox. Jay Shuster’s sketch for the forthcoming movie Cars, for example, is a lively little triptych that portrays the evolution of cow to tractor, demonstrating how the storytellers create their characters with a swirl of graphite rather than clicks of the mouse. That such traditional methods lie at the heart of Pixar’s process would have delighted Walt Disney.

Disney also knew that to conquer the box office he had to offer a tear for every laugh, arrowing his characters’ successes and failures, dreams and dilemmas right into his audiences’ hearts. It is a lesson that Pixar has learnt well; indeed, the firm’s early successes often unfold like the studio comedies that littered the box office during the 1930s and 1940s.

In fact, when creating Monsters, Inc. Pixar realised that it was in danger of subscribing to a formula. In among its tumultuous tales there was always a buddy pairing, a song about the importance of buddies and a high-octane chase at the end. As a consequence, its more recent movies — Finding Nemo, The Incredibles and, one hopes, Cars — have proved more daring in their narrative and their structure. Pixar never locks down its scripts, working instead with story reels that constantly evolve, allowing changes to be made up to the last minute.

It is an expensive choice, but one that has allowed each Pixar movie to appear on screen in a near perfect form. After all, as this wonderful show proves (and to borrow a line from Geri the Cleaner in Toy Story 2), “You can’t rush art”.

Pixar: 20 Years of Animation is at the Science Museum, SW7 (0870 8704868), from Sat