Spinks, who was diagnosed with prostate cancer in 2019, which spread to his bladder, died Friday in Henderson, Nev., which is near Lake Vegas with his wife, Brenda Glur Spinks, at his side and "only a few close friends and other family were present" because of COVID-19 restrictions.
"Leon fought his battle with numerous illnesses resiliently, never losing his trademark smile," the statement read Saturday night. "Showing true Spinks determination, he never threw in the towel."
Two years after winning an Olympic gold medal as a light heavyweight representing the United States in Montreal, Canada, in 1976, he fought Ali on Feb. 15, 1978, at the Las Vegas Hilton Pavilion with 5,300 in attendance.
The 24-year-old Spinks, weighing 97 pounds was a heavy underdog against Ali, 36 and 224 pounds. Spinks won on a 15-round split referee decision, including surviving a 15th-round flurry of punches from the defending champion.
Spinks found the strength to come back, remembering how his father would beat him.
"My dad had gone around and told people I would never be anything," Spinks told Sports Illustrated. "It hurt me. I've never forgotten it. I made up my mind that I was going to be somebody in this world. That, whatever price I had to pay, I was going to succeed at something."
After the fight, Ali said: "I recall thinking, 'That kid is a tough son of a bitch,' "
Flashing a gap-tooth grin, Spinks proclaimed: "I'm not The Greatest. Just the latest.''
Top Rank boxing, which is based in Las Vegas and run by Bob Arum, promoted the fight.
"Top Rank joins the boxing community in mourning the passing of Leon Spinks -- A true legend, who pulled off one of the greatest Heavyweight upsets of all time in 1978," the company tweeted
Spinks' career went downward after that fight.
He was stripped of the WBC title for refusing to defend against top contender Ken Norton. He fought Ali in a rematch, taking away the WBA title in a unanimous decision at the Superdome in New Orleans with a crowd of 63,000 seven months after their first bout.
In his only other heavyweight title fight, he suffered a TKO loss to Larry Holmes for the WBC belt in June 1981.
"You gave me a hell of a fight but you were a good guy," Holmes posted on Twitter. "You lived your life the way you wanted and it was a good one. I pray you Rest In Peace."
Dropping down to cruiserweight, he lost to Dwight Muhammad Qawi on a sixth-round TKO in March 1986.
He retired at 42 after losing a unanimous decision to Fred Houpe in December 1995.
His career record was 26-17-3 (14 KOs).
Spinks, who was born in Atlanta, in 2005 moved to Columbus, Neb., where he unloaded trucks and worked as a custodian at the YMC.
He moved to Las Vegas in 2011 and married Brenda. He was indicted into the Nevada Boxing Hall of Fame in 2017.
Survivors include Michael Spinks, the Hall of Fame former heavyweight and light heavyweight champion Michael; son, Cory Spunks, the former undisputed welterweight world champion; grandson Leon Spink III, who also is a professional fighter.