Regarded as one of the game's greatest in his position, Banks was named FIFA goalkeeper of the year six times and earned 73 caps for England, BBC Sport reported.
He is perhaps best known for his wonder save from Pele during the 1970 World Cup against Brazil.
Born in Sheffield, he 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," his family said.
"We are devastated to lose him but we have so many happy memories and could not have been more proud of him."
Sir Bobby Charlton, who was part of the team alongside Banks that won the World Cup in 1966, said, "Gordon was a fantastic goalkeeper, without doubt one of the best England has ever had.
"I was proud to call him a teammate. Obviously we shared that great day in 1966 but it was more than that.
"Even though I was on the pitch and have seen it many times since, I still don't know how he saved that header from Pele."
Banks is the fourth player of the England team that started the 1966 World Cup final to have died, after Bobby Moore, Ray Wilson and Alan Ball.
Former England striker Gary Lineker said, "An absolute hero of mine, and countless others, England's World Cup winner was one of the greatest goalkeepers of all time, and such a lovely, lovely man."
Ex-England goalkeeper Peter Shilton, who replaced Banks at Leicester, tweeted, "I'm devastated – today I've lost my hero."