Banks won 73 caps for England between 1963 and 1972 and made nearly 200 appearances for Stoke before his playing career was brought to an end due to a car crash that cost him the sight in one eye.
He was widely regarded as one of the greatest goalkeepers to have played the game and will be best remembered for the diving stop he made to deny Brazil's Pele at the 1970 World Cup, which later became known as the "save of the century".
"It is with great sadness that we announce that Gordon passed away peacefully overnight," Banks' family said in a statement posted on Stoke's official website.
"We are devastated to lose him but we have so many happy memories and could not have been more proud of him."
Pele rose to head a cross from the byline by right-winger Jairzinho, thundering the header down towards Banks' right hand post.
The ball appeared to be past Banks but his agility and strength saw him get down and palm it high and wide to safety.
Pele travelled to Stoke 38 years later to unveil a statue to Banks and recalled the save.
"From the moment I headed it, I was sure it had gone in," he said.
"After I headed the ball, I had already began to jump to celebrate the goal. Then I looked back and I couldn't believe it hadn't gone in. I have scored more than a thousand goals in my life and the thing people always talk to me about is the one I didn't score," he said.
Banks recalled the moment modestly as a piece of good fortune.
"As soon as I got my hand to it, I thought it was going in the top corner," he said.
"But after I'd landed on the hard floor, I looked up and saw the ball bounce behind the net and that's when I said: Banksy, you lucky prat."
Banks retired in 1973 following the car crash, aged only 33, but four years later he returned to play in the North American Soccer League with Fort Lauderdale Strikers.
The German Football Association (DFB) paid tribute to Banks on, saying on Twitter: "A fierce opponent and a good man.
Rest in peace, Gordon Banks."
(Reporting by Simon Jennings in Bengaluru; Editing by Sudipto Ganguly and Angus MacSwan)