The former Kent and Worcestershire bowler featured in 41 Tests and 36 one-day internationals for England during a 10-year international career which encompassed two Ashes wins in 1981 and 1986-87.
After retiring from the game, Dilley moved into coaching and enjoyed spells as an assistant coach with the England men's team and bowling coach to the England women's team before taking up a position as head cricket coach at Loughborough University.
"Graham made a life-long contribution to the game of cricket at all levels and we are deeply saddened by the sad news this morning. He will be fondly remembered for his contributions both as a player and a coach," said ECB chief executive David Collier.
"Few will forget his contribution during the historic Ashes win at Headingley in 1981 and the part he played in two Ashes series victories.
"Graham will be sadly missed by all his friends throughout cricket and ECB sends our deepest condolences to Graham's family."
Dilly took a total of 138 Test wickets for England.