He died Friday from complications of the fatal genetic condition, formally called Hutchinson-Gilford, ABC News reported.
His parents, Dr. Leslie Gordon and Dr. Scott Berns, announced Sam's death Saturday via the website for Progeria Research Foundation, which they founded in 1999 to find the cause of the rare disease and a cure.
"The entire [Progeria Research Foundation] community mourns the loss of this remarkable young man who not only inspired [Progeria Research Foundation]'s creation, but also touched millions of people worldwide," said the online statement.
Progeria affects approximately one child out of every 1 million to 2 million births. There are an estimated 250 children currently living with the disease, which causes the body to produce the protein progerin, which in turn causes children to lose body fat and hair and to age rapidly. The expected lifespan of someone diagnosed with progeria is about 13 years.
Sam, who was featured in the the HBO documentary, "Life According to Sam," touched the lives of ordinary people, as well as celebrities and athletes, CNN reported.
The New England Patriots, from Sam's hometown of Foxborough, Mass., held a moment of silence at the Gillette Stadium Saturday before their game against the Indianapolis Colts.
"I loved Sam Berns and am richer for having known him," Patriots owner Robert Kraft said. "He was a special young man whose inspirational story and positive outlook on life touched my heart."
"All in all, I don't waste energy feeling bad for myself," Sam said. "I surround myself with people that I want to be with. And I keep moving forward."