The S.C. Supreme Court on Friday issued an order directing the Corrections Department to carry out the sentence.
Mr. Williams, a former Evans, Ga., resident, was found guilty of the June 1991 murders of his wife, Linda, and their 12-year-old son, Shaun.
Mrs. Williams, a Bel Air Elementary School paraprofessional, was beaten to death. Shaun was strangled.
Their bodies were doused with gasoline and set afire in the family van, which was driven into a tree in Edgefield County, in what police said was a botched attempt at staging a fiery accident.