He was considered one of the finest-ever goalkeepers and, alongside his heroics in 1966, he will be remembered for the iconic save he produced against Brazil's Pele in the tournament four years later.
Banks made 73 global appearances and lifted the 1966 World Cup in England's 4-2 win over West Germany.
England's top goalscorer in World Cup finals Gary Lineker posted a heartfelt message to his "hero" Banks, while hailing him as one of the greatest to play the sport.
He also played every game of England's 1966 World Cup heroics and won the League Cup with Stoke and Leicester before retiring in 1973.
"It is with great sadness that we announce that Gordon passed away peacefully overnight, ' Banks" family said.
His family said Banks, who lost an eye in a vehicle crash in 1972, had passed away in his sleep.
"Gordon was a fantastic goalkeeper, without doubt one of the best England has ever had".
Paul Casey leads by 3 strokes over Mickelson at Pebble Beach
Former US Open victor Lucas Glover (70) and fellow American Scott Piercy (69) share third at 11 under. "He's going to be tough to catch".
"On behalf of everyone connected with England, I send my condolences to his wife Ursula, his family and friends".
A spokesperson for Leicester City, for whom Banks played 293 times during his eight-year spell with the club, wrote: "Leicester City Football Club is deeply saddened to learn of the death of our former goalkeeper Gordon Banks OBE, who has passed away at the age of 81". Sad for football, Stoke City and for England fans. RIP Gordon Banks", tweeted Leicester and England defender Harry Maguire, while Watford keeper Ben Foster said: "Had the pleasure of meeting you as an 18-year old-with my Dad, and him being completely star struck by you.
"Very sad to hear the news that Gordon has died".
Gordon Banks jumps to make a save in the match with Hungary at Wembley.
Manchester City and England midfielder, Raheem Sterling said: "Of course there was THAT save, but its so much more we are mourning today".
Fellow goalkeeper Neville Southall added: "RIP Gordon Banks A incredible keeper and it was a joy to have met and worked with him".
"I was proud to call him a team-mate".