Mills was the public face of tennis championships for over two decades, serving as the All-England Club’s referee from 1983 to 2005.
He was awarded an OBE for his services in 1996, and a CBE in 2006.
His duties included ordering play, satisfying the media, dealing with players and their agents, as well as suspending play due to weather – a role that earned him the nickname “Rain Man”.
In a statement confirming Mills’ death, the ATP described the long-time referee as having had “impeccable character and integrity”.
They added: “Mills opened his office door to every player at the All England Club and earned universal respect.
“If there was a problem, he quickly nipped it in the bud and treated every player equally – from a World No. 1 to the 128th player in the draw.”
Former Wimbledon referee, Gerry Armstrong, added: “Alan was a great influence on myself and many officials around the world.
“He was always helpful and encouraging during the years we worked together at Wimbledon and on the ATP Tour. It was a great honour to work alongside him in professional tennis for many decades.”
Several other tennis stars have paid tribute.
Australian ex-tennis referee Richard Ings said: “Sad to lose Alan Mills, a man of integrity and dignity. He was the epitome of English common sense on the world’s tennis courts.
“I loved working with him at Wimbledon, Monte Carlo. He appointed me to umpire a Wimbledon semi. I was 23. Universally respected. Thinking of his family.”
Doubles legend Pam Shriver added: “Alan Mills had just the right touch as Wimbledon referee. RIP.”
Mills had also been a legendary player in his youth, winning the Royal Air Force Tennis Championship twice, and representing Great Britain in three Davis Cup ties.
He went on to reach Wimbledon’s fourth round on two occasions, and the third round of the French Open twice.
Alongside his wife, international table tennis player Jill Rook, he also made 14 appearances in the Wimbledon mixed doubles.
Mills’ death comes just days after the respected sports journalist Mike Dickson died whilst covering the Australian Open in Melbourne.
The pair had been friends for years.
Sports journalist Stuart Fraser said: “Dicko was talking about Alan in the press room earlier this week and shared some stories from years gone by. A very sad few days.”