James played 399 games for Burnley in three spells at Turf Moor. He also spent two years at Derby County.
James played for Swansea City, Sunderland, Bury and Newport County in a 19-year career before turning to management with several clubs.
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Burnley chairman Alan Pace said: "We are sorry to hear the news of Leighton's passing.
"He left an indelible mark on this football club and stories of his playing skills still echo around Turf Moor.
"Our thoughts are with his family at this sad time."