William Steig’s career with The New Yorker began in 1930, when it first bought a cartoon from him for the rich sum of $40. At the age of 23 he had vaulted straight to the top of his profession, and his association with the magazine was to continue for more than 60 years, making him its longest-serving active contributor.

Jostling for space among the great names of the trade such as Peter Arno, Charles Addams, James Thurber and Saul Steinberg, he went on submitting half-a-dozen cartoons a week for consideration, year after year, decade after decade. The magazine printed 1,650 of them, and an astonishing tally of 117 covers.

It was through the magazine, too, that Steig embarked on his second career, when a fellow cartoonist, Bob Kraus, started the children’s publishing house Windmill Books and asked him for something to publish. Steig enjoyed inventing the letter-puzzle book C D B! (“See the Bee!”), published in 1968, and went on to write and illustrate children’s books at the rate of about one a year.

The best known of his creations for children was Shrek!, which began as a picture storybook in 1990. It was the story of a green ogre merrily scaring everything he meets and finally marrying his dream princess, a monster even uglier than he is, with whom he lives “horribly ever after”. In 2001 the book was made into an animated film by Dreamworks, and won an Oscar. Little Shreks were spawned in all directions, and although Steig had initial reservations about the film treatment, he came round to it, and particularly enjoyed the dragon-chasing.

William Steig was born in Brooklyn in 1907. His father was an immigrant house painter with artistic interests and socialist convictions who lost his job and his savings in the Depression. Unlike another housepainter of the era, back in the Europe he had left behind, Steig’s father was an idealist at the head of a happy family of four sons. One of them, Irwin, gave young William his first drawing lessons, and himself became a professional artist. All were encouraged to escape the clutches of capitalism by working in the arts, and when William found early success he used his substantial earnings — $4,500 in 1930 — to keep the family together.

His very earliest cartoons had been published in the school newspaper. He then spent two years at City College and three years at the National Academy before moving to the Yale School of Fine Arts — and dropping out after five days.

He had always loved fairy tales, legends and magic, and Charlie Chaplin, and these and the family’s optimism remained with him all his life. When one of his cartoon figures declares: “People are no damn good”, Steig means us to see this as redounding upon the little man, for the artist himself stuck to the unfashionable conviction that “people are basically good and beautiful”.

He once said that he would have liked to be “a professional athlete, a sailor, a beachcomber, or some other form of hobo, a painter, a gardener, a novelist, a banjo-player, a traveller, anything but a rich man” — and he never milked his success for cash. Having been a member of the All-American water polo team at college, he worked briefly as a lifeguard, once saving a woman’s life and being rewarded with a $1 tip. His reaction was an amused shrug.

Thanks to his stable and loving upbringing, Steig valued childhood, and pondered what it is that so often goes wrong. “Children are genuine, which is such a big problem with grown-ups,” he said. “After we’re about 30, we have to give up being children.” His longest-running series of New Yorker drawings, reflecting his own experiences in street gangs, was Small Fry, in which mischievous urchins draw attention to the strange behaviour of their seniors by imitating it, or look on bewildered by the neurosis that is adulthood.

Steig’s sentimentalised children often have to keep their thoughts to themselves, but he implies that their boisterous, freewheeling way is the truer one, while the adults are misled by thoughts of dignity or authority. A mother looking in on her wideawake child bawls: “Sleep!” It’s not the child who is crying.

The titles of some of his dozen or so collections pose their own questions: Strutters and Fretters, Our Miserable Life, Agony and the Kindergarten — why must it be so? How did the magic of childhood give way to the insecurity of men and women? “Neurosis is the biggest obstacle to peace and happiness”, Steig commented, and he was a sucker for the pseudo-scientific theories of Wilhelm Reich, a Freudian psychologist who was later jailed, about the power of “orgone”, universal orgasmic energy. Until the end of his life Steig would regularly sit in an elaborate phone-box contraption called an orgone accumulator to top himself up. His longevity suggests that it was at least an effective placebo.

Steig’s first cartoon collection, About People, appeared as early as 1939, and he was always in demand as a cartoonist, but like his idol Picasso, he enjoyed looking for other means of expression too, and took to carving figures in wood.

A collection of symbolic drawings of states of pain entitled The Lonely Ones (1942) was considered a breakthrough and remained in print for 25 years. The drawings appeared on all kinds of spin-off goods, and this led Steig (overcoming his distaste) into advertising. He also drew a series of tongue-in-cheek greetings cards, producing a revolution in the industry. Steig had become part of the American mainstream, and was extravagantly praised by contemporaries from W. H. Auden and e. e. cummings to Harpo Marx.

But though he might be admired as a satirist, Steig’s philosophy was hardly challenging, rarely actually causing offence. The exception that proved the rule was Sylvester and the Magic Pebble (1969), the tale of a donkey who turns into a stone. When Sylvester goes missing, his parents go to the police, whom Steig showed as uniformed pigs. The International Conference of Police Associations was unamused and stuck in its trotter. There was a burst of outrage, with several God-fearing states removing copies of the book from libraries.

But this was naivety rather than Orwellian satire, and Steig wrote to The New York Times: “I am not the kind of man who would trouble children with political propaganda.” The storm blew over and Steig won the Caldecott Medal.

More books followed, more animals and more awards — Steig’s first novel for children, Dominic, won the Christopher in 1972. In all they achieved worldwide sales approaching two million. When he had turned 90, The World of William Steig, with an introduction by John Updike, brought together work for children and for adults and showed an oeuvre full of humour and hope.

“I feel a complete lack of art spirit in our culture now,” he said 15 years ago. “It’s all talk of war, and everyone wants to get rich and be safe, surrounded with money bags and chicken fat. The worst feeling is knowing you haven’t lived the life you were meant to live, that we all were meant to live.” Steig’s last book, When Everybody Wore a Hat, appeared in June and was another return to childhood. He for one had kept the faith.

William Steig is survived by his fourth wife, Jeanne Doron, an artist whom he married in 1968, and by a son and daughter from his first marriage and a daughter from his second.

William Steig, artist and writer, was born on November 14, 1907. He died on October 3, 2003, aged 95.