Born in Sheffield, Banks spent the majority of his club career with Leicester City and Stoke City, winning the League Cup with both eight years apart, before retiring in 1973, having lost sight in his right eye as the result of a vehicle crash.
Leicester City - one of his former clubs - posted they were saddened to hear of the news, while existing Foxes man Harry Maguire called Banks "a legend".
Former England forward Sir Bobby Charlton, who played alongside Banks in the 1966 final, said: "Gordon was a fantastic goalkeeper, without doubt one of the best England has ever had".
Former England striker Gary Lineker said: "An absolute hero of mine, and countless others, England's World Cup victor was one of the greatest goalkeepers of all time, and such a lovely, lovely man".
Fellow ex-England global Ray Parlour, meanwhile, hailed his save against Pele as the "best ever": 'More sad news in the football world.
We, at Soccer Laduma, send our condolences to the family and friends of Gordon Banks. Legend Gordon Banks passes away aged 81. Greatest English keeper to have ever lived?
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He will always be remembered for a remarkable save he made to deny Brazil superstar Pele four years later in Mexico. "Really sad news. Growing up, one of the featured pieces of commentary I consistently heard was "that" save".
Another supporter said: "What a sad, sad day".
Banks started his career at Chesterfield, before moving to Leicester City, for whom he played 293 times.
England and Manchester City forward Raheem Sterling was among the first to pay tribute, tweeting: "Of course there was that save, but it's so much more we are mourning today".
Former England and Leicester striker, Gary Lineker wrote on social media: "Oh no. Gordon Banks, an absolute hero of mine, and countless others, has died".