The multimillionaire singer confirmed his resignation this week in a letter to chairman Graham Simpson, under whose watch the club has slipped from the Premier League to 21st in the second tier and lost promising young manager Adrian Boothroyd.
Boothroyd, who left the club on Monday by mutual consent, is a friend of John's.
"Elton wishes the team every success for the future," said a statement on John's official Web site.
"However, in the light of developments over the past few months, he feels he cannot remain in any formal position within the club."
John was accorded the honorary title in recognition of his long association with the club, which he took over as chairman in 1976 and guided to the top division.
The club was runner-up to Liverpool in 1983 and lost the 1984 FA Cup final to Everton.
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