His sons Nathan and Griffith confirmed in a Facebook post the actor died on Friday following complications from diabetes.
Furst's other film credits included comedies Midnight Madness and The Dream Team, and he had recurring TV roles in St Elsewhere and Babylon 5.
"Steve has a long list of earthly accomplishments," the statement said.
"He was known to the world as a brilliant and prolific actor and film-maker, but to his family and many dear friends he was also a beloved husband, father and kind friend whose memory will always be a blessing."
It continued: "To truly honour him, do not cry for the loss of Stephen Furst. But rather, enjoy memories of all the times he made you snicker, laugh, or even snort to your own embarrassment.
"He intensely believed that laugher is the best therapy, and he would want us to practice that now."
Furst had type 2 diabetes, which his son Nathan told CNN had been getting worse over recent years.
Furst's fans and co-stars paid tribute to the actor on Twitter, with Animal House star Tim Matheson writing: "We loved ya, pal. Rest in peace."
America's Got Talent judge Howie Mandel said: "I am heartbroken to learn of the passing of my friend Stephen Furst. A kind heart, great talent and beautiful human being."
Writer and director Edgar Wright wrote: "Oh boy, was he great. Farewell Flounder. RIP Stephen Furst."
And director Kevin Smith tweeted: "As an awkward round kid, Flounder was the Delta I most identified with in #AnimalHouse, my fave comedy. #StephenFurst helped shape who I am."
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Actor Stephen Furst, who was best known for playing Flounder in Animal House, has died at the age of 63.