Banks won 73 caps for England between 1963 and 1972 and made almost 200 appearances for Stoke before his playing career was brought to an end due to a vehicle crash that cost him the sight in one eye.
According to BBC Football, the goalkeeper's family issued a public statement on Banks' death.
"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'.
"Gordon will be deeply missed and our thoughts are with his family at this very sad time. Even though I was on the pitch I still don't know how he saved that header from Pele".
Banks started his career at Chesterfield, before joining Leicester in 1959 for £7,000, and it was at the Foxes that he established himself as England's number one, earning his first global cap in 1963 against Scotland.
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Banks was named FWA Footballer of the Year in 1972, and was named FIFA Goalkeeper of the Year on six occasions.
Banks started his career at Chesterfield, before moving to Leicester City, for whom he played 293 times.
Banks is also remembered for winning the 1972 League Cup with Stoke, in what remains to be the club's only major trophy.
This accident cost him his sight in his right eye, as well his professional career at the age of 34.
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".
Manchester City and England midfielder, Raheem Sterling said: "Of course there was THAT save, but its so much more we are mourning today".
"On behalf of everyone connected with England, I send my condolences to his wife Ursula, his family and friends".