Spinks had been battling multiple types of cancers, including prostate cancer, for years, according to a spokesperson.
"Rest in peace, Leon Spinks," World Boxing Council President Mauricio Sulaiman tweeted Saturday evening. "Olympic medalist, Pan American medalist, and of course, WBC heavyweight champion."
Spinks defeated defending champ Ali in 1978 in just his eighth professional fight, shocking the boxing world and taking the world heavyweight championship after a split decision in Las Vegas, Nevada. It remains one of the biggest upsets in boxing history.
"Ali thought I was a wimp, and I had to prove to him I wasn’t," Spinks said in 2014. "I knew I could beat him after watching his fights."
In a rematch later that year, Ali took back the belt in New Orleans.
He took Olympic gold in Montreal in 1976. His younger brother Michael won a gold medal in a separate weight class the same year.
Spinks had a second title shot in 1981 against Larry Holmes but fell short in the third round. Michael Spinks later claimed the belt from Holmes in 1985, losing it to Mike Tyson three years later in his final fight.
Leon Spinks finished his career with a 26-17-3 record, including 14 wins by knockout.
He was inducted into the National Boxing Hall of Fame in 2016.
Spinks has battled several health issues over the last decade. He was diagnosed with brain shrinkage in 2012, a condition doctors said stemmed from the beatings he took in the ring, and in 2014 he was hospitalized for abdominal problems.
Fox News’ Ryan Gaydos and Morgan Phillips and the Associated Press contributed to this report.