Wilson was diagnosed with Alzheimer's disease in 2004 and passed away in Huddersfield on Tuesday.
Football Association chairman Greg Clarke said in a statement: "We are extremely saddened to hear the news about Ray Wilson.
"A wonderful player who was so well thought of across the game, Ray will forever be remembered for achieving a remarkable Wembley double in 1966.
"In one summer, he helped Everton win the FA Cup just weeks before being part of the England team that won the World Cup.
"A true great of English football, our thoughts are with his wife Pat, his family and friends."
We are shocked and saddened to hear of the passing of World Cup winner Ray Wilson. Our thoughts are with his family and friends. pic.twitter.com/DwPzzrDlda— The FA (@FA) May 16, 2018
Wilson's former England team-mate Bobby Charlton said: "Lady Norma and I are deeply saddened by the awful news that Ray has passed away.
"Ray was an excellent team-mate at international level for many years and a close friend. We shared some wonderful memories throughout our career and I had the pleasure of being his room-mate.
"Ray was a great man and he will be missed by so many people."
#htafc is devastated to learn of the passing of @England World Cup winner Ramon ‘Ray’ Wilson MBE at the age of 83.— Huddersfield Town (@htafcdotcom) May 16, 2018
The thoughts of everyone at Town are with Ray’s wife, his sons and the rest of his family and friends at this difficult time.
https://t.co/ojODZDyi0R (AT) pic.twitter.com/tq661fFWJn
Wilson's former clubs Everton, Huddersfield Town, Oldham Athletic and Bradford City all paid tribute.