The 6-4, 230-pound Webb committed in January to play at Colorado. However, because he was still enrolled at Texas Tech for the spring semester, his commitment was nonbinding.
Darrin Chiaverini, who recruited Webb for Colorado, took to Twitter on Wednesday to say he supported Webb's decision.
Webb himself has NFL potential. ESPN draft guru Mel Kiper Jr. ranks Webb as his No. 1 senior quarterback prospect.
Sources told ESPN that Webb began to have a change of heart in February, around the time that Cal coach Sonny Dykes hired Jake Spavital as the team's new offensive coordinator and quarterbacks coach.
Spavital is from Mike Leach's "Air Raid" coaching tree, as is Dykes and Texas Tech coach Kliff Kingsbury.
Dykes' pass-heavy offensive system is similar to the one in which Webb threw for 5,557 yards and had 46 touchdowns (22 interceptions) over three seasons with the Red Raiders. Webb started the bulk of games over his first two seasons before being overtaken by current starter Patrick Mahomes, a rising NFL draft prospect.
Some of those departures were offset by the recent announcement that ESPN 300 receiver Demetris Robertson had picked the Bears over Georgia and Notre Dame. He will enroll this summer.
With Goff in Dykes' offense a year ago, Cal was seventh in the country in yards per play and 17th in scoring. Two years removed from a 1-11 season, the Bears went 8-5 and returned to a bowl game for the first time since 2011.