Hutchins, who had suffered from motor neurone disease, played professionally and spent 13 years as Davis Cup captain, taking Britain to the 1978 final against the United States.
"Paul was an extraordinary man, colleague and friend," Richard Lewis, chief executive of the AELTC, said in a statement.
"As my Davis Cup captain, he was a great leader, had extraordinary attention to detail, and always had the best of intentions when dealing with everyone in tennis."
Hutchins served a number of roles in British tennis, including a stint as the LTA's Head of Men's Tennis, team leader of Britain's 2012 London Olympics tennis squad and tournament director of the Nottingham championships.
(Reporting by Martyn Herman, editing by Ed Osmond)
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