Webb is scheduled to graduate from Texas Tech this spring and will be able to play immediately for the Buffaloes as a senior graduate transfer.
"It's a good fit, and I felt comfortable with the staff," Webb told ESPN.com. "I'm looking forward to competing for playing time and being a great teammate."
Webb also took to Twitter on Wednesday to express his excitement over joining the Buffaloes.
— Davis Webb (@Davis_Webb7) January 27, 2016
Webb started a total of 14 games for the Red Raiders in 2013 and 2014, throwing for 5,557 yards and 46 touchdowns during his three seasons in Lubbock. Webb backed up Patrick Mahomes this season after starting eight games in 2014.
Colorado recently hired Texas Tech assistant Darrin Chiaverini as its new co-offensive coordinator, and he hosted Webb on an official visit to CU on Jan. 16.
"I felt wanted as a player and felt like I was getting a fair chance to compete," Webb said. "The players and coaches are great men, and I look forward to working with them."
The Buffaloes lost starting quarterback Sefo Liufau to a season-ending Lisfranc injury in November, and he could miss the 2016 season.