The 21-year-old threw for 5,557 yards, 46 touchdowns and 22 interceptions in 23 games over three seasons at Texas Tech, but lost his spot atop the depth chart to Patrick Mahomes, the team's current starter.
Webb figures to have a good shot of earning the starting job for Cal.
His coach at Texas Tech, Kliff Kingsbury, described Webb in 2014 as "one of those top-five pick talents."
"He has a chance to be very special," Kingsbury told FOX Sports. "He has one of the quickest releases and strongest arms I've been around. Very smart, intellectual thinker. Processes things very quickly. Sees the field. Great at checking to the right place."
If Webb comes anywhere close to living up to that billing, Cal will have plenty to be proud of on draft night for the second straight year.