They were among six people to be initiated at a ceremony this week at the World Golf Village in Florida, the others being Hutchison's fellow double major champion Doug Ford, Japanese legend Jumbo Ozaki and the late Frank Chirkinian, who made his name in the game as a television producer.
Along with Ford, Hutchison was elected in the Lifetime Achievement category and his place among some of the game's greatest names is a fitting reward for the successful career he carved out in America after leaving Scotland at an early age.
Born on 6 June 1884, he emigrated to the States in the early 1900s, settling in Pittsburgh at the Allegheny Country Club. By 1918, he was at Glen View Club in the Village of Golf, Illinois. In 1919, he became a PGA professional and, in 1920, he earned his US citizenship.
He recorded 14 wins in his career, including the 1920 PGA Championship and the 1921 Open Championship, returning to St Andrews to become the first player to take the Claret Jug back across the Atlantic. During the opening round he had a hole-in-one at the eighth and then narrowly missed back-to-back aces after driving the 278-yard ninth, catching the corner of the cup and lipping out to within inches.
Hutchison's victory at the Old Course - he beat Englishman Roger Wethered by nine shots in a play-off - was also notable for the grooved clubs which he used to get spin and master the hard greens. His triumph came on 25 June, just before a ban on such clubs was imposed by the R&A's Rules of Golf Committee.
"I'm glad to get home," Hutchison was quoted as saying as he emerged from the ocean liner Carmania, leading a group of eight Americans off the ship, before he produced the Claret Jug for the small crowd of fans who gathered for their arrival. "Well, here it is," he added.
Hutchison might have underplayed the historic victory, but the press on both sides of the Atlantic ran huge headlines. They trumpeted Hutchison becoming the first player to take golf's oldest championship trophy outside of Europe.
A two-time Western Open champion, he also won the inaugural Senior PGA Championship in 1937, which was held at Augusta National, and again in 1947.Talking of Augusta National, Hutchison was the first honorary starter at The Masters (along with Fred McLeod) from 1963 to 1973.
His addition to the Hall of Fame, nearly 34 years after he passed away, reunites "The American Triumvirate" as Hutchison, Walter Hagen and Jim Barnes were dubbed after they won a combined 71 times - including 17 major championships - on the fledgling American professional circuit in the early 1900s.
"In competition," wrote the legendary Herbert Warren Wind of Hutchison, "he was dourness itself and as nervous as a mosquito. He walked around restlessly between shots. He sweated lavishly and took to waving his arms in the air to dry them. He literally twiddled his thumbs . . . (But] when he shifted into a brilliant streak, Jock could play one plus-perfect hole after another, each shot, like mountain views in Switzerland, seemingly more breathtaking than the one that went before."
Each Hall of Fame inductee is given a locker to fill with artifacts and personal memorabilia and Hutchison's featured items include the "mashie iron" he used at St Andrews in 1921, his winner's medal from that event and the one from the 1937 Senior PGA Championship.
Membership of the Hall of Fame now stands at 136, with Hutchison joining the likes of Tommy Armour, Willie Anderson, James Braid, Old Tom Morris, Young Tom Morris, Willie Park senior, Allan Robertson and Donald Ross on the list of Scottish-born people to be inducted.
"This is a special night," said World Golf Hall of Fame chief operating officer Jack Peter. "The 'Class of 2011' comes from South Africa, Japan, the United States and Scotland. The global nature of this wonderful class embodies so much of what the World Golf Hall of Fame stands for. We are thrilled to welcome all of them into the Hall of Fame family."
Three-time major winner Els, the first active player to be inducted since Vijay Singh in 2006, was elected on the PGA Tour ballot, Ozaki, winner of more than 100 tournaments, was voted in through the International ballot while Bush and Chirkinian were both selected through the Lifetime Achievement category.
Players must be at least 40 to be considered for the Hall of Fame, and Els, whose locker items include the set of irons he used to win the 2002 Open Championship at Muirfield, was voted in on his first try. The South African, who is playing in The Players Championship this week at TPC Sawgrass, said: "I think it will be a very special feeling to step on the first tee knowing you've made the Hall of Fame.
"You don't get inducted in here without doing something to catch people's attention, whether it's winning 18 or 19 majors like Jack Nicklaus or building golf courses like Pete Dye. There are people here that have done special things in the game of golf. I feel I've won my fair share of tournaments around the world, a truly global golfer like my idol, Gary Player."Bush, who becomes the second US president in the Hall of Fame, joining 2009 inductee Dwight D Eisenhower, was selected for helping to raise the profile of golf by serving as honorary chairman of the Presidents Cup.
Chirkinian died of cancer in March, just three weeks after learning he had been selected for induction. He was the foremost golf producer at CBS Sports, leading its coverage of the Masters for nearly four decades. Among his innovations were installing a camera on the blimp and using scores in relation to par to show who was leading tournaments.