His eldest son, musician and cartoonist Peter Blegvad, said his father died on Jan. 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."
He also collaborated with his wife, Lenore Blegvad, who wrote numerous children's books that he illustrated until her death in 2008, and his lifelong friend, fellow Dane N.M. Bodecker. Blegvad published his own memoir, "Self Portrait," in 1979.
Critics were often entranced by his work and seemed to run out of adjectives praising his drawings, often falling back on "witty" and "charming". A 1996 review in The Washington Post called him a "modern master" for his illustration of Andersen's famous tales.
While he was an art student during the Nazi occupation of Denmark, Blegvad and a friend were arrested with a suitcase full of leaflets printed by the Danish resistance.
He later split his time between London and the United States, contributing to many American magazines and spending much of his time in South Wardsboro, VT.
He is survived by his children, Peter and Kristoffer, and four grandchildren.