Shebbeare, who became the trust's first chief executive in 1988, will now take up a new position as director of charities in the Prince of Wales' household.
Fred Goodwin, chairman of the trust, said Shebbeare "must take much of the credit for building the organisation that there is today".
Shebbeare, who was knighted in 2003's New Year honours list, said: "I have enjoyed the past 15 years enormously."
Recruitment for a replacement will begin this month.
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