Family spokeswoman Marci Robinson said Kemp died shortly after 6 p.m. Saturday, surrounded by his family. Kemp died at his home in Bethesda, Md., in the Washington suburbs, friends said.
Kemp's office announced in January that he had been diagnosed with an unspecified type of cancer. By then, however, the cancer was in an advanced stage and had spread to several organs, former campaign adviser Edwin J. Feulner said. He did not know the origin of the cancer.
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.
Feulner, president of The Heritage Foundation, a Kemp family friend and his former campaign deputy chief of staff, said Kemp's legacy will be his compassion.
"The idea that all conservatives really should regroup around and identify with is that this is not an exclusive club," Feulner said. "Freedom is for everybody. That's what Jack Kemp really stood for."
Praise rolled in from fellow politicians.
Newt Gingrich told CBS News correspondent Kimberly Dozier that Kemp was key to helping the Republican party into a new position.
"He was second only to Reagan in teaching us to be optimistic," Gingrich told Dozier. "In teaching us that economic growth and jobs was the key to our future, in teaching us that lower tax rates encouraged entrepreneurs, increased everybody's wealth and led to a better future."
Senate Republican leader Mitch McConnell, R-Ky., called Kemp "one of the nation's most distinguished public servants. Jack was a powerful voice in American politics for more than four decades."
Former President George W. Bush expressed his sorrow after hearing of Kemp's death.
"Laura and I are saddened by the death of Jack Kemp," he said. "Jack will be remembered for his significant contributions to the Reagan revolution and his steadfast dedication to conservative principles during his long and distinguished career in public service. Jack's wife Joanne and the rest of the Kemp family are in our thoughts and prayers."
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.
Kemp led Buffalo to the 1964 and 1965 AFL Championships, and won the league's most valuable player award in 1965. He co-founded the AFL Players Association in 1964 and was elected president of the union for five terms. When he retired from football in 1969, Kemp had enough support in blue-collar Buffalo and its suburbs to win an open congressional seat.
In 11 seasons, he sustained a dozen concussions, two broken ankles and a crushed hand - which Kemp insisted a doctor permanently set in a passing position so that he could continue to play.
"Pro football gave me a good perspective," he was quoted as saying. "When I entered the political arena, I had already been booed, cheered, cut, sold, traded, and hung in effigy."
NFL Commissioner Roger Goodell said "Kemp was an extraordinary American leader who became a trusted colleague and exceptional friend to countless NFL owners, team personnel and commissioners after his MVP playing career with the Buffalo Bills."
Kemp was born in California to Christian Scientist parents. He worked on the loading docks of his father's trucking company as a boy before majoring in physical education at Occidental College, where he led the nation's small colleges in passing.
He became a Presbyterian after marrying his college sweetheart, Joanne Main. The couple had four children, including two sons who played professional football. He joined with a son and son-in-law to form a Washington strategic consulting firm, Kemp Partners, after leaving office.
Through his political life, Kemp's positions spanned the social spectrum: He opposed abortion and supported school prayer, yet appealed to liberals with his outreach toward minorities and compassion for the poor. He pushed for immigration reform to include a guest-worker program and status for the illegal immigrants already here.