Tillis, 85, died at Munroe Regional Medical Center in Ocala, Fla.
Respiratory failure was the suspected cause, but the singer had suffered from intestinal issues since early 2016.
Tillis wrote hits for Kenny Rogers, Ricky Skaggs and many more.
Under his own name, he cut six singles that topped the country charts, including "I Ain't Never", "Coca-Cola Cowboy" and "Southern Rains". He wrote some of country music's most compelling and consequential songs, he fronted a remarkable band, and he sang with power and emotion.
Tillis was a familiar screen presence in the '70s and '80s, with small roles in films including "W.W. and the Dixie Dancekings", "The Villain", "Every Which Way But Loose", "Smokey and the Bandit II", and both "Cannonball Run" movies.
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Additionally, Tillis had other hits such as Stateside, I Got the Hoss, Send Me Down to Tucson, Neon Rose, Sawmill and Midnight, Me and the Blues.
He was awarded the National Medal of Arts for his contributions to country music by President Obama in 2012. It wasn't a commercial success, but the group was nominated for vocal event of the year by the Country Music Association. He also briefly co-hosted an ABC prime-time series, "Mel and Susan Together", with supermodel Susan Anton in 1978. He developed the stutter as a child after a bout with malaria.
In 2007, Tillis became a regular performer on the Grand Ole Opry country music show.
His first big hit as a songwriter was "I'm exhausted", which was recorded that same year by Webb Pierce, who went on to record several more of Tillis's compositions. His family plans to announce funeral arrangements in Nashville and Florida soon.
Tillis appeared on several television shows, including "Hee Haw" and "Hollywood Squares".