"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 on Wednesday 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.
Nieto sits second in the all-time list of most motorcycling world championship titles, two behind Italian great Giacomo Agostini.
Only Agostini and current Italy great Valentino Rossi have bettered his tally of 90 Grand Prix victories.
Spanish compatriot and current world MotoGP champion Marc Marquez was amongst the first to pay tribute to Nieto, who also grabbed 139 podium places in his career.
"Thanks for everything you have taught us! Rest in peace maestro," the three-time MotoGP world champion tweeted.
Football giants Real Madrid also remembered Nieto.
"Real Madrid are deeply saddened by the passing of Angel Nieto and extend their condolences to his family and friends at this difficult time," the European champions tweeted.
"Spanish sport has lost a true legend who will never be forgotten. His extraordinarily successful career and exemplary behaviour have made him an eternal idol for motorcycle fans around the world and for sport in general."
Nieto competed in his first Grand Prix at just 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.
"The day I decided to stop racing I was 39, it had been two years since I had won the last world championship and I was in Austria," Nieto recalled in an interview with Spanish broadcaster TVE.
"The mechanics left and I thought 'what am I doing here, I said this is it, the winning spirit I always had had come to an end. When it was over, I got down, I said I'm going home, and it was over."
However, he still remained involved in the sport as team manager when Emilio Alzamora won the 125cc world championship in 1999.
"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.
Mi pésame a la familia de Ángel Nieto, leyenda del motociclismo y del deporte español que supo ganarse el respeto y cariño de la afición. MR— Mariano Rajoy Brey (@marianorajoy) August 3, 2017