Spurrier and two assistants, quarterbacks coach G.A. Mangus and running backs coach Everette Sands, visited Williams at school early last month. Mangus previously coached at Delaware Valley, Widener, and Ursinus.
"Just from the beginning of the recruiting process, they've been there strong," Williams said.
"They've been at my house. Coach Spurrier has shown a lot of interest. That stood out for me."
With Tuesday's 33-28 victory over Michigan in the Outback Bowl, the Gamecocks (11-2) matched the program record for victories in a season. They went 6-2 in the Southeastern Conference.
South Carolina's leading rusher, Marcus Lattimore, is giving up his final season to enter the NFL draft. The junior missed the final four games of this season because of a knee injury.
"David is excited about coming in and getting the chance to play right away," Crosby said. "That was one of the factors in his decision."
In eight years with the Gamecocks, Spurrier, 67, is 66-37. In 23 college seasons, he is 208-77-2, with seven SEC titles.
Williams' only official visit was to Arizona State. The Sun Devils, guided by Todd Graham, went 8-5 in 2012, including a 62-28 romp over Navy in the Fight Hunger Bowl.
Earlier this week, Larry Porter, who coached Arizona State's running backs and was involved in the recruiting of Williams, left to serve in the same role at Texas.
In the fall, Williams, a four-star recruit who has been clocked at 4.4 seconds in the 40-yard dash, rushed for 1,799 yards and 23 touchdowns in helping lead the Panthers to a 14-1 record and the PIAA Class AA state semifinals.
For his career, the 18-year-old, who spent two seasons at West Catholic and one at North Catholic, totaled 4,700 rushing yards and 58 touchdowns.
Williams was joined at the Semper Fidelis game in Carson, Calif., by Penn Charter lineman Mike McGlinchey, Roman Catholic wideout Will Fuller, and George Washington defensive end Justin Moody.
Contact Rick O'Brien
or @ozoneinq on Twitter. Read his blog, "The O'Zone,"