The man known as ‘The King’ in honour of the way he popularised the game passed away in Pittsburgh on Sunday.
The news is set to overshadow the 41st Ryder Cup, which gets underway at Hazeltine on Friday.
As tributes poured in, former world No 1 Tiger Woods took to Twitter to pay his respects to the seven-time major winner.
“Thanks Arnold for your friendship, counsel and a lot of laughs. Your philanthropy and humility are part of your legend,” wrote Woods on the social media site.
“It’s hard to imagine golf without you or anyone more important to the game than the King.”
Palmer racked up 95 worldwide tournament wins, including back-to-back Open Championship victories in 1961 and 1962.
His failing health was evident at The Masters earlier this year, when he joined Jack Nicklaus and Gary Player, the other members of the so-called “Big Three”, on the first tee at Augusta National but was unable to hit a shot in his role as one of the event’s honorary starters.
“Arnold is the reason golf enjoys the popularity it does today,” said Nicklaus, then game’s greatest player.
“He made golf attractive to the television-viewing public. There never has been anyone like him before in the game of golf, and there probably won’t be another like him again.”
R&A chief executive Martin Slumbers added: “It is with great sadness that we have awoken to hear the news of Arnold Palmer’s passing. He was a true gentleman, one of the greatest ever to play the game and a truly iconic figure in sport.
“His contribution to The Open Championship was, and remains, immeasurable. He will be missed and forever remembered by all at The R&A and throughout the world of golf as a charismatic and global champion of our game.”
Davis Love, the Team USA captain, at Hazeltine, added: “When I think of Arnold Palmer, I think of his natural ability to relate to people, the close bond he had with his father, and how when I first came on Tour, he made young professionals like me feel welcome.
Like me, Mr Palmer was born the son of a PGA Professional and was taught by his dad not only the fundamentals, but also how to give back to this great game. He leaves an impact on the game and on sports in America that is unmatched.
“Our country lost a great sportsman, a great American. As we approach the Ryder Cup this week, our team will keep Mr Palmer’s family in our prayers and will draw from his strength and determination to inspire us.”