His spokeswoman Bona Park and longtime friend and former campaign adviser Edwin J. Feulner confirmed that Kemp died after a lengthy illness.
Kemp had announced in January 2009 that he had been diagnosed with cancer. He said he was undergoing tests but gave no other detail.
Senate Republican leader Mitch McConnell called Kemp "one of the nation's most distinguished public servants, Jack was a powerful voice in American politics for more than four decades."
Kemp, a former quarterback for the Buffalo Bills, represented western New York for nine terms in Congress, leaving the House for an unsuccessful presidential bid in 1988.
Eight years later, after serving a term as President George H.W. Bush's housing secretary, he made it onto the national ticket as Bob Dole's running-mate.
With that loss, the Republican bowed out of political office, but not out of politics. In speaking engagements and a syndicated column, he continued to advocate for the tax reform and supply-side policies -- the idea that the more taxes are cut the more the economy will grow -- that he pioneered.
Kemp's rapid and wordy style made the enthusiastic speaker with the neatly side-parted white hair a favorite on the lecture circuit, and a millionaire. (His style didn't win over everyone. In his memoirs, former Vice President Dan Quayle wrote that at Cabinet meetings, Bush would be irked by Kemp's habit of going off on tangents and not making "any discernible point.")
Kemp also signed on with numerous educational and corporate boards and charitable organizations, including NFL Charities, which kept him connected to his football roots.
Kemp was a 17th round 1957 NFL draft pick by the Detroit Lions but was cut before the season began. After being released by three more NFL teams and the Canadian Football League over the next three years, he joined the American Football League's Los Angeles Chargers as a free agent in 1960. A waivers foul-up two years later would land him with the Buffalo Bills, who got him at the bargain basement price of $100.
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