He contributed to the magazine for several decades, drawing many portraits of its mascot Alfred E Neuman.
MAD art director Sam Viviano said Davis` "immediately recognisable style revolutionised comic illustration".
`One of the greats`
A spokesman for the magazine, which began as a comic book in 1952, said a list of his "most legendary pieces would run to several pages in length".
He added: "Among his most iconic parodies from MAD`s comic book days are of The Lone Ranger and High Noon.
"From the magazine, his notable parodies include spoofs of Raiders of the Lost Ark, Gone with the Wind, and M*A*S*H."
The magazine`s editor John Ficarra said there "wasn`t anything Jack couldn`t do".
"Front covers, caricatures, sports scenes, monsters - his comedic range was just incredible.
"His ability to put energy and motion into his drawings, his use of cross-hatching and brush work, and his bold use of colour made him truly one of the greats."
Davis began his career at the University of Georgia, where he drew for the campus newspaper - his depictions of the athletics teams, the Georgia Bulldogs, still grace the walls of the institution.
The university`s alumni association tweeted that Davis would be "missed by the Bulldog family".
Georgia radio station WGAU said Davis` first success after university was to illustrate a Coca-Cola training manual, "a job that gave him enough cash to buy a car and drive to New York".
Once there, he worked as a freelance cartoonist, before finding a role with EC Comics, contributing to a number of their titles, including Tales From The Crypt and Incredible Science Fiction.
The editors of those titles - William M Gaines, Albert B Feldstein and Harvey Kurtzman - went on to launch MAD, which Davis contributed to from the start as one of the "Usual Gang of Idiots", the magazine`s spokesman said.
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