Ralph Collier, a shark expert, said tooth fragments were discovered that appear to be from the lower jaw of a great white, probably one 15 to 16 feet long, the San Diego Union-Tribune reported.
David Martin of Solana Beach bled to death Friday morning. He was swimming with other members of the Triathlon Club of San Diego.
The great white is one of the most feared ocean predators and is believed responsible for almost 90 percent of the shark attacks in California. There have been 31 reported shark attacks since 2000, with two deaths.
Authorities closed 8 miles of the coast to swimming for 72 hours after the attack.
George Burgess, director of the International Shark Attack File at the Florida Museum of Natural History, said there are many theories on why sharks attack.
"White sharks are a natural part of the marine environment in the waters off San Diego," Burgess said. "Humans are not owed 100 percent safety when we go into the ocean. The ocean is a wilderness. It's not a chlorinated swimming pool."