Taback died of pancreatic cancer Dec. 25 at his home in Ventura, said his son, Jason.
His breakthrough book as an author-illustrator, "There Was an Old Lady Who Swallowed a Fly," has been described as "a tour de force in innovative book illustration and design" and was a 1998 Caldecott Honor Book.
For his retelling of the tale, Taback used die cuts to show the growing contents of the old woman's expanding stomach as she eats larger and larger animals. He also added new rhymes and side comments from the animals.
"When the art came in, everybody was so dazzled," recalled Regina Hayes, publisher of Viking Children's Books, which published his two best-known books and other titles.
"Die cuts had been used many times in novelty books but never had been done with such artistry," said Hayes. "Instead of treating it like a novelty book, we gave it the highest production values because we were so impressed by the quality of the art."
Taback also used die cuts for "Joseph Had a Little Overcoat," which won the Caldecott Medal in 2000.
The tale follows a Polish peasant, who frugally creates new uses for his deteriorating plaid overcoat, which goes from being a jacket to a vest, a scarf, a tie, a handkerchief and, finally, a button. Then the button is lost, and there is nothing.
But even then, the resourceful Joseph created a book about the experience that provides the moral of the story: "You can always make something from nothing."
Taback, whose first language was Yiddish, drew upon his own cultural heritage in creating the book.
"Simms was notable for his seemingly naive but actually very sophisticated art and for his distinctive use of color and design, and he drew on a folkloric tradition but with his own sophistication," Hayes said.
Taback was a founding president of the Illustrators Guild in New York City and a founding member and president of the New York Graphic Artists Guild.
"He had a real concern for other artists; he just cared about making sure they were recognized and their rights were upheld," said Hayes. "He was larger than life in every way. He had this enormous talent as an artist, but also he had the biggest, most generous heart."
Reynold Ruffins, an illustrator and designer with whom Taback formed a studio in 1963 and later launched a greeting card company, said Taback's "personality was reflected in his work," particularly in his children's books.
"There's a sense of humor, and the books deal with warm feelings and generosity between people," said Ruffins.
Taback spent about 30 years in advertising as an illustrator, designer and art director. Among his clients were American Express, Pepsi, Kentucky Fried Chicken and NBC.
His original sketches for the first McDonald's Happy Meal box in 1976 are in a collection at the Smithsonian Institution.
Despite his acclaim as an author-illustrator of children's books, Taback's Happy Meal box proved to be his most impressive credit to some young readers.
As he recalled in 2009 in the Ventura County Star: "I used to visit schools and the kids would be half asleep and, when I told them about that, they would go, 'Wow!'"
The son of eastern European immigrants, Taback was born in New York City on Feb. 13, 1932, and grew up in the Bronx.
He attended New York's High School of Music and Art and graduated from the Cooper Union for the Advancement of Science and Art in 1953. He launched his career after serving two years in the Army.
Taback also taught illustration and design at the School of Visual Arts in New York and at Syracuse University.
In 2006, he and his wife, Gail, moved from their home in Woodstock, N.Y., to Ventura.
His most recent children's book, "Postcards from Camp," was published in June.
A retrospective of his work, "Simms Taback: Making Pictures for Children," at the Museum of Ventura County is on display through Feb. 12.
In addition to his wife and son, Taback is survived by his daughter, Lisa Deane; his step-daughter, Emily Kuenstler; and five grandchildren.