Arnold "passed away peacefully, surrounded by loved ones, in his sleep after his courageous battle with cancer", the band said on Instagram.
3 Doors Down formed in Mississippi in 1995 and four years later received a Grammy nomination for the breakout hit Kryptonite. Arnold wrote the song in maths class when he was just 15, the band said.
Their debut album, The Better Life, sold more than six million copies. A second Grammy nomination came in 2003, for the song When I'm Gone.
Arnold "helped redefine mainstream rock music, blending post-grunge accessibility with emotionally direct songwriting and lyrical themes that resonated with everyday listeners," the band said.
3 Doors Down released six albums, most recently Us And The Night in 2016.
Singles included Loser, Duck and Run and Be Like That, which appeared on the soundtrack for the 2001 film American Pie 2.
While promoting their 5th album, Time of My Life, Arnold said he considered himself lucky to have carved out a career in the music business.
"If you do something as long as we've done it, you can't help but get better at it, you know?" Arnold told The Associated Press in 2011.
In 2017, 3 Doors Down performed at the first inauguration concert of President Donald Trump.
Arnold announced his cancer diagnosis last May, saying clear cell renal carcinoma had metastasised to his lungs. The band was forced to cancel a summer tour.
"His music reverberated far beyond the stage, creating moments of connection, joy, faith, and shared experiences that will live on long after the stages he performed on," the band said.
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