Tillis, 85, died at Munroe Regional Medical Center in Ocala, Fla.
His suspected cause of death is respiratory failure, after he was battling an intestinal issue since 2016.
Tillis, a father of six who endeared fans with his stammer and self-deprecating charm, recorded more than 60 albums, scored 35 top 10 singles, and saw 600 of his songs recorded by major artists during a career spanning six decades.
His No. 1 songs were I Ain't Never, Good Woman Blues, Heart Healer, I Believe in You, Coca-Cola Cowboy and Southern Rains.
From Tim McGraw, "Man, one of the coolest guys in country music ever and an extraordinary songwriter!"
He also dabbled in acting, appearing in such feature films as Clint Eastwood's "Every Which Way But Loose", and the Burt Reynolds movies "Cannonball Run I and II" and "Smokey and the Bandit II". "It's a way of showing people that it hasn't licked me, so it doesn't have to lick others".
In 2011, Tillis was named a National Medal of Arts recipient for his contributions to country music, the Tennessean reported. He was also a member of the Grand Ole Opry and a Nashville Songwriters Hall of Fame inductee.
"You know what? Another part of the dream has been fulfilled", he said at the time.
Tillis was raised in Pahokee, Florida, and developed his stutter as a child while being treated for malaria. He started performing in the early 50s with a group called The Westerners.
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.
Funeral arrangements have not yet been announced. His stutter became a trademark that Tillis mined for laughs, although it disappeared when he sang.