He passed away at his home in Scottsdale, Arizona, just four days after he publicly announced that he was losing his fight with the disease and was close to death.
Killebrew had said doctors told him the cancer was incurable and that he had stopped taking medication because he wanted to spend his final days in hospice care.
I have exhausted all options with respect to controlling this awful disease, he said in last week's statement.
His death came swiftly and peacefully, with his wife Nita and other members of their family by his side, the Hall of Fame and Minnesota Twins, the team he was long associated with, said in a joint statement.
The tributes began immediately after the news of his death was announced.
Harmon was a beacon of light among his fellow Hall of Famers, always smiling, always enjoying every moment that life delivered at his doorstep, said Jane Forbes Clark, Chairman of the National Baseball Hall of Fame and Museum.
We have so many fond memories of this wonderful baseball hero, and we will miss him enormously.
Killebrew was an 11-times All-Star whose 573 career home runs are the 11th most in Major League Baseball. He was nicknamed Killer because of his deadly prowess with the bat, a moniker which belied his soft-spoken demeanor off the field.
He was so down-to-earth, you would never realize he was a baseball legend, said Hall of Fame President Jeff Idelson. It's ironic that his nickname was 'Killer,' as he was one of the nicest, most generous individuals to ever walk the earth.
Killebrew signed with the former Washington Senators, who moved to Minnesota in 1961 and became the Twins. He remained with the organization until playing his final year with the Kansas City Royals in 1975.
A powerful hitter who was second only to Babe Ruth for American League home runs when he retired, was named the AL's Most Valuable Player in 1969 after a season where he recorded a career-best 140 RBIs, 49 home runs and a .276 batting average while playing in all 162 of Minnesota's games that year.
The Twins retired his uniform number in 1975 and he was inducted into the Hall of Fame in 1984 after a 22-year career in which he recorded 1,584 RBIs and a .256 batting average in 2,435 games.
No individual has ever meant more to the Minnesota Twins organization and millions of fans across Twins Territory than Harmon Killebrew, said Twins President Dave St. Peter.
Harmon will long be remembered as one of the most prolific home run hitters in the history of the game and the leader of a group of players who helped lay the foundation for the long-term success of the Twins franchise and Major League Baseball in the Upper Midwest.