He had Lou Gehrig's disease, and the governing body of men's tennis said in a statement he died at his home in Sydney.
Drewett was a top-40 singles and top-20 doubles player before he retired in 1990. He was hired in 2006 to lead operations in the Middle East, Asia and the Pacific regions. He led the ATP since January 2012.
"Our thoughts are with Brad's family on this extremely sad day for them, the ATP and the entire international tennis community," the ATP said in a statement. "He will be sorely missed by all."
International Tennis Federation President Francesco Ricci Bitti called Drewett "a valued friend and colleague."
"We were very happy to support him during his various roles at the ATP, most recently as chairman," he said. "His knowledge, experience and enthusiasm will be a great loss to the whole sport."
Players Rafael Nadal and Mardy Fish were among those expressing condolences.
"A very sad day for the world of sports and tennis in particular," Nadal, an 11-time major champion, wrote on Facebook. "Our president Brad has passed away. Rest in peace."
A moment of silence was observed Friday at the draw ceremony for the Mutua Madrid Open. The Portugal Open will hold a one-minute silence Saturday on center court before the first men's semifinal.
Drewett announced in January he had motor neurone disease or amyotrophic lateral sclerosis. The disease affects voluntary muscle activity, including speaking, walking, breathing and swallowing. It usually causes progressive disability.
Drewett's speech was noticeably slurred when he attended a news conference on the opening day of the Australian Open to announce a new sponsor. He had planned to step down once a successor was found.
Drewett also developed and managed a number of successful businesses in the sport and fitness industry. He had worked as a commentator for two Australian television broadcasters.
"The tennis world lost a strong leader, true gentleman and a great friend," U.S. Tennis Association Chairman and President David Haggerty said.
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