"The 13-time world champion -- whose superstition always referred to his titles as 12+1 - was a MotoGP legend and a key figure in establishing Spain as a world-beating force in Grand Prix motorcycle racing," the official site of the motorcycling world championship said.
Nieto was on a quad bike yesterday last week when he "had an accident with a tourism vehicle," police said at the time.
He was rushed to hospital in a serious state where he remained in intensive care, but his condition deteriorated before passing away.
Only Agostini and current Italy great Valentino Rossi have bettered his tally of 90 Grand Prix victories.
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"My condolences to the family of Angel Nieto, a legend of motorcycling and Spanish sport, who won the respect and love of the fans," Spanish prime minister Mariano Rajoy tweeted.
Nieto competed in his first Grand Prix when at just was 17 in 1964 before going on to win six world titles in the 50cc category and seven in the 125 division.
He retired aged 39 two years after his final world championship in 1986.