"It is with great sadness that we announce that Gordon passed away peacefully overnight", the statement was quoted, as saying by BBC Football.
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 worldwide cap in 1963 against Scotland.
"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".
Fellow ex-England worldwide Ray Parlour, meanwhile, hailed his save against Pele as the "best ever": 'More sad news in the football world. 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. Legend Gordon Banks passes away aged 81. Obviously we shared 1966 but it was more than that. Still the best save ever from Pelé header'. The Great Gordon Banks'.
'RIP Gordon banks, what a goalkeeper and a lovely fella too #gkunion, ' Crossley posted.
A spokesperson for Chesterfield FC, where Banks began his career in the 1950s, said: "The sad news reaches us that legendary former Spireite Gordon Banks has passed away". He was my first Goalkeeper Coach when I was a school boy at @swfc when Jack Charlton was manager.
"I was proud to call him a teammate".
England's official Twitter account wrote: "We're deeply saddened to hear that Gordon Banks, our #WorldCup-winning goalkeeper, has passed away".
An inspiration, a victor and a true gentleman.
We, at Soccer Laduma, send our condolences to the family and friends of Gordon Banks.