The United States Golf Association also confirmed his death in a tweet calling him "golf`s greatest ambassador".
During a long career he won more than 90 tournaments worldwide, including seven majors.
Arnold Palmer was the most important golfer to play the game, said the BBC`s golf correspondent Iain Carter.
His force of charisma put the game on the map and it never dimmed, he added.
Fellow golfing great and a close friend of Palmer, Jack Nicklaus said he would "miss him greatly".
"We just lost one of the incredible people in the game of golf and in all of sports," he tweeted.
"Arnold transcended the game of golf. He was more than a golfer or even great golfer. He was an icon. He was a legend."
Palmer attracted thousands of diehard fans known as "Arnie`s Army" and helped to promote the game into the television age.
"Today marks the passing of an era," said Alastair Johnston, CEO of Arnold Palmer Enterprises.
"Arnold Palmer`s influence, profile and achievements spread far beyond the game of golf. He was an iconic American who treated people with respect and warmth, and built a unique legacy through his ability to engage with fans."
Tributes to the sporting star flooded in from the world of golf.
"Thanks Arnold for your friendship, counsel and a lot of laughs. Your philanthropy and humility are part of your legend," Tiger Woods tweeted.
"Remembering the special times I spent with Mr Palmer at Bay Hill. A true pioneer for our sport. Forever remembered," said Northern Ireland`s Rory McIlroy, hours after winning the Tour Championship in Atlanta.
"My heart aches with passing of the King. What he did for golf cannot be measured. Athlete, pioneer, philanthropist, family man, and much more...RIP Arnie," tweeted US golfer Zach Johnson.
Tributes also came in from outside the golf world.
US President Barack Obama tweeted a picture of himself with Arnold Palmer at the White House, adding: "Here`s to The King who was as extraordinary on the links as he was generous to others. Thanks for the memories, Arnold."
Palmer was born in Latrobe, Pennsylvania, in 1929, the son of a groundskeeper at the local country club who later became the professional at the golf club there.
He was one of golf`s most dominant players in the late 1950s and early 1960s, winning seven major titles over seven seasons.
He also notched up 62 PGA Tour wins.
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