Mills, a four-times Olympic athlete and former Auckland mayor, and his wife, Colleen, founded the first Les Mills gym on Victoria Street in central Auckland after a sporting career in which Mills represented New Zealand in shot put and discus.
More than five decades later, Les Mills workouts - a bar-bell based weight training class designed to tone and strengthened using moderate weights and high repetitions - are used by clubs around the world.
The business, now run by later generations of the Mills family, became internationally known for choreographed group-exercise classes set to music.
Mills' son, Phillip, joined the business full-time in 1980 and his partner, Jackie, helped develop the music-driven group-fitness model that became central to its global expansion.
Phillip Mills said in a statement on Monday that his father had achieved a huge amount in his life but the common thread was he always wanted to help others.
"Dad was immensely strong, driven, and always cared deeply for the less advantaged. He left a lasting impression on everyone he met, and his spirit lives on in gym workouts around the world, continuing to help people fall in love with fitness," he said.
Mills was born Leslie Roy Mills in Auckland in 1934. He competed at four Olympic Games from 1960 to 1972 and won five Commonwealth Games medals, including discus gold at the 1966 British Empire and Commonwealth Games in Kingston, Jamaica.
He later moved into local politics and served as mayor of Auckland from 1990 to 1998.
He also remained active in sport as a coach, helping guide New Zealand discus thrower Beatrice Faumuina to the world title in 1997 and Commonwealth Games gold in 1998.
Mills was appointed a Member of the Order of the British Empire in 1973 for services to sport and a Companion of the New Zealand Order of Merit in 2002 for services to local government and sport.
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