"We are devastated to lose him but we have so many happy memories and could not have been more proud of him."
Banks played 73 times for England and featured in every match of the 1966 tournament which culminated in a 4-2 win in the final against West Germany.
The German football federation led the tributes on Tuesday. "A fierce opponent and a good man," it tweeted.
Geoff Hurst, who scored a hat-trick in the triumph at Wembley, tweeted: "Very sad to hear the news that Gordon has died. One of the very greatest."
After hoisting the World Cup in 1966, his most illustrious personal moment came four years later in the 1970 tournament in Mexico.
During a group stage game against Brazil in Guadalajara, he miraculously kept out a goal-bound header from the Brazil striker Pele. It has been described as one of the greatest saves of all time.
"Once I got my hand to it I hadn't a clue where it was going," Banks said later.
Pele admitted he was certain the ball was heading into the net.
Teammate Alan Mullery recounted: "I patted Gordon on his head and I said: 'Why didn't you catch it?' ... And the abuse that came back was unbelievable."
Mullery said Banks was probably the best goalkeeper he had played with or against.
"We had some great goalkeepers in those days," said Mullery. "And the only person I can think of who came near was Pat Jennings. Gordon was an absolutely marvellous goalkeeper. He was a likeable man, and when it came to business, he was probably the best there has ever been."
Banks's domestic haul of trophies was modest by comparison. He won the League Cup at Leicester City and at Stoke.
Stoke City chairman, Peter Coates, said of Banks - who played 250 times for the club after he joined from Leicester in 1967 - "It's a very sad day for us. We love him so much.
"He made his home in Stoke and was very much part of the fabric of the club. You don't get too many like him, and he was immensely modest for all his talent."