Stiles had suffered from advanced dementia and prostate cancer.
A statement from the Stiles family read: “The Stiles family are sad to announce that Nobby Stiles passed away peacefully today surrounded by his family after a long illness.
“The family kindly ask for privacy at this sad time.”
Stiles made 28 international appearances for England and was part of the 1966 winning squad.
He also won two league titles and the 1968 European Cup during his 11-year spell with United.
The England national team paid tribute to Stiles on social media: “We’re incredibly saddened to learn of the passing of Nobby Stiles, a key member of our @FIFAWorldCup winning squad, at the age of 78.
“All of our thoughts are with Nobby’s loved ones.”
Manchester United also released a statement which read: “We are extremely saddened to learn of the passing of Nobby Stiles MBE.
“An integral part of our first-ever European Cup-winning side, Nobby was a titan of the club’s history, cherished for his heart and personality on and off the pitch. He will be sorely missed by us all.”