KSBY-TV, Santa Barbara, reported the Santa Barbara County Sheriff's Office identified the victim as Francisco Javier Solorio Jr., 39, of Orcutt. Solorio was bitten in the upper torso, the sheriff's office said.
Andrew Nosal of the Scripps Institute of Oceanography told the Los Angeles Times great whites are responsible for nearly all shark attacks off California's coast.
"If indeed it was a shark, it was probably a great white," Nosal said. "There is no other species swimming off of the coast regularly that could possibly do that kind of damage."
Lt. Erik Raney of the sheriff's office said Solorio's surfboard had visible signs of bite marks.
Federal and state wildlife officials are also working to identify the type of shark.
Solorio was attacked just before 11 a.m. off Vandenberg Air Force Base.
The Times said it was the 13th fatal shark attack in California waters since 1950 and the sixth since 2003.