Webb, a 14-game starter during his three seasons at Texas Tech, is scheduled to graduate from Texas Tech this spring and would enroll at his new school in the summer. He will be eligible to play in 2016, when he will be a senior.
"Davis Webb is the hardest-working individual I've ever had the privilege of coaching," Texas Tech head coach Kliff Kingsbury said in a statement. "He's a fierce competitor and an extremely talented quarterback. Wherever Davis lands, he will immediately change the outlook of that program. All Red Raider fans should be extremely proud of what he's accomplished here in Lubbock and look forward to watching him compete next season."
Webb threw for 5,557 yards and 46 touchdowns during his stint in Lubbock and was the Red Raiders' starter for their first eight games of 2014 before suffering a season-ending shoulder injury. He served as Patrick Mahomes' backup this year.
"I look forward to graduating this spring, and I will immediately begin the process of finding a place that fits me both academically and athletically," Webb wrote on his Twitter account.
Webb's decision to transfer was amicable and long expected after Mahomes won the job and accounted for 5,109 total yards and 46 touchdowns this season as a sophomore.