Grant had a heart attack Friday while working at the drawing board in his Glendale home studio, according to a statement released by Walt Disney Co.
Grant's time at Disney spanned more than six decades, starting with his work on early movies like "Snow White" in 1937 and culminating with later films like "Pocahontas" in 1998 and "Lorenzo," a short feature released in theaters just last year. He was named an official Disney legend at a ceremony in 1992.
"With his vast knowledge of art and literature, Grant was considered the studio's top intellectual and he had a profound influence on the films that got made," the company's statement said.
Grant, who began his career as a caricaturist for the Los Angeles Record, was hired by Walt Disney in 1933 to work on the animated short "Mickey's Gala Premiere."
He was later tapped to design the queen-witch character in "Snow White" and was made head of a department that served as a think tank for future animated projects, including "Pinocchio" and "Fantasia."
Grant also co-wrote "Dumbo" and conceived "Lady and the Tramp" with his wife.
He left the company in 1949 to start his own businesses, but returned to Disney 40 years later to work on "Aladdin," "The Lion King," "Pocahontas" and "Mulan."
"We were so incredibly fortunate to have had Joe at the studio sharing his creativity and enthusiasm, and inspiring young talent for such a long time," said David Stainton, president of Walt Disney Feature Animation.
More than 70 of Grant's caricatures are included in the permanent collection at the Smithsonian Institute and he received a Ruben Award from the National Cartoonists Society in 1996.
Grant is survived by two daughters. His wife of 70 years, Jennie, died in 1991.