"He had been suffering from Parkinson's disease for more than four years and lost his brave battle at home in Melbourne surrounded by family," a statement said.
Thomson was the first Australian to win the British Open, claiming the famous claret jug on five occasions between 1954 and 1965, including three consecutive wins. Only American Tom Watson in the modern era has matched the feat.
While he won dozens of tournaments in Europe, Australia and Asia, Thomson only played a few seasons in the United States, winning the Texas Open in 1956. But he did tee-off more regularly on the American senior circuit, winning nine times in 1985, setting a record that may never be broken.
As well as being a great player, he was an outstanding contributor to the game.
Thomson served as president of the Australian PGA for 32 years, designing and building courses in Australia and around the world.
He also helped establish the Asian Tour and wrote for newspapers and magazines for 60 years. He was patron of the Australian Golf Writers Association.
Fellow Australian and seven-time major winner Karrie Webb called him an "Aussie legend and true gentleman of the game".
"My heart goes out to his wife Mary and the rest of the Thomson family. So honoured to have been able to call Peter my friend. RIP Peter," she tweeted.
The World Golf Hall of Fame called him "the thinking man's golfer".
"His style was free of the extraneous, so that the path he would take to victory seemed a remarkably straight line.
"With his confident gait and serene smile, he had the self-possessed aura of a winner."
Born in Melbourne, Thomson won the Victorian Amateur Championship before beginning his professional career in 1949, initially concentrating on the European circuit and the British courses that he loved.
The Victoria Golf Club, which he joined in 1946 and was a life member, said he was a true star.
"As well as being a champion on course, he was incredibly well-respected throughout the world golfing community. A truly great round!" it tweeted.
Thomson was made Commander of the Order of the British Empire (CBE) in 1979 for his service to golf, and in 2001 became an Officer of the Order of Australia (AO) for his contributions as a player and administrator and for community service.
He is survived by his wife Mary, a son and three daughters, 11 grandchildren and four great-grandchildren.
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