The band's manager, Robert Hayes, said Harwell "passed peacefully and comfortably" on Monday morning surrounded by family and friends at his home in Boise, Idaho. The cause of death was acute liver failure, Hayes said in a statement.
Smash Mouth is also known for hits including "Walkin' On The Sun and Then The Morning Comes.
"Steve Harwell was a true American Original. A larger than life character who shot up into the sky like a Roman candle," Hayes said.
"Steve should be remembered for his unwavering focus and impassioned determination to reach the heights of pop stardom."
"His only tools were his irrepressible charm and charisma, his fearlessly reckless ambition," Hayes said, adding: "Steve lived a 100 per cent full-throttle life. Burning brightly across the universe before burning out."
"He will be greatly missed by those who knew and loved him," he said.
Born in California in 1967, Harwell performed in a rap group called F.O.S. (Freedom of Speech) before forming Smash Mouth in 1994. The band released two platinum albums on Interscope Records, their ska-fuelled 1997 debut and 1999's Astro Lounge. The second album featured some of the band's biggest hits, including the Grammy-nominated, platinum single All Star, which appeared in the movie Shrek alongside their cover of the Monkees' I'm a Believer.
Humour was a driving force behind Smash Mouth's success, and at the forefront was Harwell's playful alt-rock voice and persona. He made a cameo in 2001 comedy film Rat Race, and had a well-documented friendship with the Food Network chef and host Guy Fieri.
On Monday, tributes began pouring in. Fieri wrote on Instagram: "To my brutha Steve RIP. Today is a sad day, I will miss my friend."
NSYNC 's Chris Kirkpatrick and Joey Fatone also shared short homages.
"I'm truly sorry for the difficult battle you had to fight," Kirkpatrick posted on Instagram. "You were an amazing soul and will be deeply missed."
Fatone said he had known Harwell for a long time.
"Opened for NSync and even was my wedding singer at my wedding," wrote Fatone.
"Hopefully people out there that are dealing with addiction. get the right help that they need."
TV host Carson Daly published a two-part statement on Instagram, detailing the first time he met Harwell in 1995, when he was a DJ on JOME in San Jose and Smash Mouth was a new band.
"In better days, Steve was a force of a frontman & lived the life of 50 men," Daly wrote.
"He brought joy to millions with his music and his legacy will thankfully live on."
"Rest in peace Steve Harwell," comedian Tom Green tweeted.
"I remember hanging with you back in the MTV days you were always super cool and an amazing talent - my condolences to your family and friends."
Harwell retired from performing and left Smash Mouth in 2021. The band continued to tour with Zach Goode as the singer and released a statement at the time saying Harwell had been diagnosed with cardiomyopathy eight years earlier.
He had suffered "nonstop serious medical setbacks including heart failure as well as acute Wernicke Encephalopathy".
Harwell will be cremated in Boise and buried in San Jose, California, alongside his mother, Hayes said.
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