Banks was part of the England team that won the 1966 World Cup and was credited with making the 'Save of the Century' when he denied Brazilian great Pele at the tournament four years later.
His death was confirmed by his former club Stoke City which tweeted a statement from his family.
'It is with great sadness that we announce that Gordon passed away peacefully overnight,' the statement read.
'We are devastated to lose him but we have so many happy memories and could not have been more proud of him.'
Banks, who revealed in 2016 that he was battling kidney cancer for the second time, was widely considered as one of the greatest goalkeepers of his generation.
He was named Fifa goalkeeper of the year six times and earned 73 caps for England.
Banks was a hugely loved and respected figure within the world of football.
He played in every game of England's run to the 1966 World Cup final which culminated in a 4-2 victory over West Germany.
But it was four years later in Guadalajara, Mexico, that Banks produced one of football's most historic saves.
Facing the legendary 1970 Brazilian side, he produced an astonishing save to prevent Pele's header from finding the net.
Recalling the save years later, Banks said: 'As I got to my feet, Pelé came up to me and patted me on the back. 'I thought that was a goal,' he said. 'You and me both,' I replied. The TV footage of the game shows me laughing as I turn to take up my position for the corner. I was laughing at what Bobby Moore had just said to me. 'You're getting too old Banksy, you used to hold on to them.' Like hell I did.'
On Tuesday, Pele wrote his own heartfelt tribute to Banks, the two having become inextricably linked through that moment in Mexico.
'I scored so many goals in my life, but many people, when they meet me, always ask me about that save,' Pele wrote on his Facebook page Tuesday.
'While it was indeed phenomenal, my memory of Gordon is not defined by that - it is defined by his friendship. He was a kind and warm man who gave so much to people.
'So I am glad he saved my header - because that act was the start of a friendship between us that I will always treasure. Whenever we met, it was always like we had never been apart.
'I have great sadness in my heart today and I send condolences to the family he was so proud of.
'Rest in peace, my friend. Yes, you were a goalkeeper with magic. But you were also so much more. You were a fine human being.'
Banks made his name at Leicester City, earning his first England cap in 1963 against Scotland.
He appeared in two FA Cup finals and won the League Cup in 1964 before joining Stoke City in 1967. It was there that he helped the club win the 1927 League Cup.
A car crash in October 1972 led to him losing the sight in his right eye and he retired in the summer of 1973.
Banks went on to enjoy a career in coaching and was named club president of Stoke City in 2002. A statue of him holding the World Cup trophy was unveiled outside the club's stadium in 2008.
He is survived by his wife Ursula and their three children, Robert, Wendy and Julia.
Tributes to Banks poured in from the world of football within minutes of the announcement of his passing.
'An all-time great for England, I was privileged enough to be in his company on a number of occasions,' England manager Gareth Southgate said in a statement.
'It was particularly special to be with him at a Football Writers' tribute dinner last year and wish him well on his 80th birthday.
'Gordon spoke to the room about that incredible save from Pele against Brazil back in 1970 and moments like that from his remarkable World Cup-winning career will continue to linger long in the memory.
Former England striker Gary Linkeker tweeted: 'Oh no. Gordon Banks, an absolute hero of mine, and countless others, has died. @England's World Cup winner was one of the greatest goalkeepers of all time, and such a lovely, lovely man. #RIPGordon.'
Ex-England forward Michael Owen called Banks 'one of the game's true gentlemen.'
Manchester City star Raheem Sterling tweeted: 'Of course there was THAT save, but its so much more we are mourning today. RIP Gordon Banks. @England legend, your legacy will live on. All my thoughts with the family.'
On Twitter, the English Football Association said: 'We're deeply saddened to hear that Gordon Banks, our #WorldCup-winning goalkeeper, has passed away. Our thoughts are with Gordon's friends, family and supporters at this difficult time.'
The German Football Association passed on its condolences, tweeting: 'A fierce opponent and a good man. Rest in peace Gordon Banks.'
Peter Schmeichel, one of the greatest goalkeepers of his own generation, also paid tribute to Banks, calling him 'an inspiration, a winner and a true gentleman.'
The German Football Association passed on its condolences, tweeting: 'A fierce opponent and a good man. Rest in peace Gordon Banks.' Recalling the save years later, Banks said: 'As I got to my feet, Pelé came up to me and patted me on the back. 'I thought that was a goal,' he said. 'You and me both,' I replied. The TV footage of the game shows me laughing as I turn to take up my position for the corner. I was laughing at what Bobby Moore had just said to me. 'You're getting too old Banksy, you used to hold on to them.' Like hell I did.'