The rock star passed away "peacefully and comfortably" on Monday morning - surrounded by his friends and family at his home in Boise, Idaho, his agent confirmed to Sky News.
Harwell had recently been receiving hospice care for liver failure and had also suffered from heart and neurological conditions in recent years.
His manager Robert Hayes told Sky News the singer was "a true American Original" - calling him "a larger-than-life character who shot up into the sky like a Roman candle".
A statement added:
"Steve has been retired from Smash Mouth for two years now, and the band continues to tour with new vocalist Zach Goode. That said, Steve's legacy will live on through the music.
"With Steve, Smash Mouth has sold over 10 million albums worldwide and topped the charts with two No 1 hit singles, five Top 40 singles, three Hot 100 singles, four Billboard 200 albums and a Grammy nomination - not to mention the hundreds of film and television placements, and of course those musical features in Shrek!
"Steve's iconic voice is one of the most recognisable voices from his generation. He loved the fans and loved to perform."
Mr Hayes added:
"Steve should be remembered for his unwavering focus and impassioned determination to reach the heights of pop stardom. And the fact that he achieved this near-impossible goal with very limited musical experience makes his accomplishments all the more remarkable.
"His only tools were his irrepressible charm and charisma, his fearlessly reckless ambition, and his king-size cojones. Steve lived a 100% full-throttle life. Burning brightly across the universe before burning out.
"Good night Heevo Veev. Rest in peace knowing you aimed for the stars, and magically hit your target."
The band had hits across the late 90s and early 2000s, with their songs All Star and their cover of The Monkees I'm A Believer bookending the 2001 DreamWorks movie Shrek - bringing them to a whole new audience.
They also appeared in cult noughties movie Rat Race, performing their track All Star at the film's conclusion.
https://news.sky.com/story/steve-harwell-smash-mouth-frontman-dies-aged-56-12955045