Armfield, who played 627 matches in 17 years for his only club and was part of the World Cup-winning squad in 1966, was diagnosed with cancer for a second time last year.
"Blackpool Football Club is deeply saddened to learn of the passing of its record appearance holder and vice-president Jimmy Armfield at the age of 82," said a statement from the club.
Armfield captained Blackpool for more than 10 of his 17 years at the club and was capped 43 times for England, with 15 of those occasions as skipper.
Only players who were on the pitch in the final received winners' medals but that was rectified 43 years later when Armfield eventually received his medal.
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Armfield had stints in management with Bolton and Leeds before moving into broadcasting where he spent more than 30 years working for the BBC.
He was inducted into Blackpool's Hall of Fame in 2006 and Bloomfield Road's newly constructed South Stand was named in his honour in 2010.
"Jimmy had two great loves, first and foremost was his family, to which he was devoted and loved dearly. The other was football, especially Blackpool, England and his colleagues at the PFA (Professional Footballers' Association)," it added.
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