Davis, 59, died today at his Plantation home, surrounded by family, Karla Guadamuz-Davis said.
His diagnosis of stage four lung cancer in February just before his birthday came as a shock because he had never smoked, she said.
The cancer spread to his liver, and the family chose to discontinue treatment in a hospital this week.
"We decided to bring him home," Guadamuz-Davis said. "He was in my arms."
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His mother died three days before the Montreal Games, and he considered withdrawing. Instead, he stayed, and dedicated his lightweight gold medal to his mother's memory.
"It was devastating," Davis told the New York Post in August. "But I remembered her pointing her finger in my face and telling me, 'You'd better win the gold medal.' I wasn't going to be denied. There was no way I was going to lose."
Davis was considered by many to be better than Leonard on the star-studded 1976 American team. As a pro, however, his career never matched his Olympic exploits.
Ten years later, a highway landscaper came across a piece of metal while at work. He cleaned it up and used it for a paperweight for the next four years.
In 1991, a visitor to the landscaper's home recognized the paperweight for what it was. The landscaper, Jake Fiesel, tracked down Davis and called him. The boxer was finally reunited with his medal.
Davis went on to train mixed martial arts fighters, including Chuck Liddell, who posted an image of an undated Polaroid showing him with Davis on his Instagram account on yesterday.
"A great coach and good friend. Rest in peace my brother," Liddell wrote.