Co-owner Sam Maw says Stroble died Monday after a fall at his home earlier this month.
Stroble had worked at the Beacon for more than 50 years, taking customers' orders and yelling instructions to the cooks.
Part of a street near the Beacon was named for Stroble in 2011. Diagnosed with glaucoma decades ago, a foundation also bears his name.
Funeral arrangements for Stroble have not been announced.
The Beacon is famous for its sweet iced tea and "a-plenty" plates that feature sandwiches topped with french fries and onion rings. It has become a popular stop for candidates in the months leading up to South Carolina's presidential primaries.