His son, musician and cartoonist Peter Blegvad, said his father died on January 14.
The wide-ranging artist was a native of Denmark who studied at the Copenhagen School of Arts and Crafts before developing his reputation in the New York and Paris publishing worlds.
He worked as a commercial illustrator and developed a sophisticated pen and ink style that seemed perfectly suited for children's books.
Among his best known works are the illustrations for "Bed-Knob and Broomstick," "The Tenth Good Thing About Barney" and his own translation of Hans Christian Andersen's "Stories and Fairy Tales."