Drewett took up his post at the top of men's tennis at the start of 2012 but it was announced in January he was suffering from Motor Neurone Disease and would be standing down.
A statement read: "The ATP is deeply saddened to announce that Brad Drewett passed away at his home in Sydney, Australia, earlier on Friday.
"Brad, who served as ATP executive chairman and president since January 2012, had been suffering from Motor Neurone Disease. Our thoughts are with Brad's family on this extremely sad day for them, the ATP and the entire international tennis community. He will be sorely missed by all."
Australian Drewett reached a career high of 34 in the world rankings in 1984, eight years after making the quarter-finals of the Australian Open as a 17-year-old.
He was a member of the ATP Player Council during the 1990s before moving on to oversee the ATP's operations in the Middle East, Asia and the Pacific, while he was also tournament director of the ATP World Tour Finals.
During his time at the head of the ATP, the body has helped negotiate big increases in prize money at all the grand slams, most recently a 40 per cent hike at this year's Wimbledon.
The world of tennis has been quick to pay tribute to Drewett, with Rafael Nadal writing on his Facebook page: "A very sad (day) for the World of Sports and tennis in particular. Our president Brad has passed away. Rest in peace."
Lawn Tennis Association chief executive Roger Draper praised Drewett for his role in helping boost the profile of the World Tour Finals.
Draper said: "Everyone in British tennis will be deeply saddened by the news of Brad's passing. He was held in the highest esteem by everyone in the tennis world.
"Brad always put the players and the sport at the heart of everything he did and his legacy will endure.
"He was a great friend to British tennis and helped to grow the Barclays ATP World Tour Finals into the most successful indoor tennis event we have ever seen. All our thoughts are with his family."
Former players Ivan Ljubicic and Justin Gimelstob, both of whom have been heavily involved with the ATP, paid tribute to Drewett on Twitter.
Ljubicic said: "Brad. Thank you for everything you did for our sport. Thank you thank you thank you. This is just not fair. Nothing else to add. R.I.P"
Gimelstob, who was elected to the ATP Board of Directors in 2008, said: "Incredibly sad day, @ATPWorldTour President Brad Drewett passed away, my deepest condolences to both his immediate and tennis family
"Brad Drewett was a great leader and the ultimate @ATPWorldTour contributor, devoted to his family, friends, and the sport he loved
"Brad, you will always be missed but never forgotten. We all owe you a debt of gratitude and never ending appreciation. Love You, RIP"
Stacey Allaster, chief executive of the WTA, believes Drewett has left a lasting legacy on the sport.
"Brad was an incredibly warm human being and a dedicated family man. He also was always an inspiring leader," she said in a statement.
"Today [Friday] the entire tennis community mourns the loss of a great friend and colleague. Brad's contributions as a player and visionary leader make him one of the greatest in making tennis the popular, worldwide sport it is today.
"The recent prize money increases with the Grand Slams are perfect examples of Brad's brilliant strategic management, and another example of how much he cared about our athletes and the sport's long-term growth.
"His legacy as a leader, as a person, and as a father who always put his family first, will have an everlasting impact on tennis.
"Our prayers go out to his wife Jo and his children Jack, Ally, Joe and Tom, and to the entire ATP family."