Webb passed away on Oct. 31 at New Hanover Regional Medical Center in Wilmington following complications of open-heart surgery, according to a Facebook post made Saturday morning.
In 1978, Raleigh had its first taste of Snoopy's Hot Dogs when it first opened at an old gas station located on the corner of Wake Forest Road and Whitaker Mill Road, according to the restaurant's website.
The restaurant would later go on to expand, opening five other locations in the Raleigh-area.
"Snoopy's was always on his mind and in his heart," the post wrote. "He greatly appreciated the loyalty of our customers over the years, and nothing delighted him more than to go somewhere and hear someone say, "I just love Snoopy's!"
His family asks in lieu of flowers, that donations be made to the Muscular Dystrophy Association or the SPCA of Wake County.