Dr Cracknell's daughter Cynthia posted on Facebook that her father died in Hawaii, in the United States, on October 24.
He is believed to have died from an illness. He is understood to have returned to America earlier this year after becoming ill.
The American was a well-known personality on the island.
A doctor of acupuncture and naturopathic medicine, with a PHD in complimentary alternative medicine, Dr Cracknell ran the Wellness House detox and naturopathic health centre alongside the Living Food Cafe in Naiharn. He moved to Phuket in 1994 after two years living in northern Thailand teaching English.
Working for many years on the island as a chiropractor, acupuncturist and general health healer, he established the Wellness House around four years ago. The Living Food Café came about from him wanting to make good food for himself and his guests, and teach others how to do the same, he told The Phuket News in an earlier interview.
Dr Cracknell also was a top regional marathon runner, regularly winning in his age group in marathons held around Southeast Asia.
Martin Smetsers told The Phuket News he met Dr Cracknell around three years ago.
"He was a dedicated health professional who knew what he was doing; a true sportsman who's vegetarian regime helped him to recover so much more quickly from big athletic events, he told me. He was devoted to the health cause; an ambassador for his beliefs and a true athlete.
"I was very sorry to hear that he got ill and was saddened by today's news. Condolences to his family; a good man has left us."
Phuket resident Sylvie Madison said, "Richard lived life to the fullest: surfing, biking, running and doing triathlons. He was an inspiration to many people and will be missed.
"His sudden illness was a big mystery here and people simply wished him good health. It is with great sadness I say goodbye to my friend."
Dr Cracknell has adult children in America and one young daughter living in Phuket.