Kelly also had been considering the vacant Florida job, sources previously told ESPN.
The decision by Kelly to move away from the Gators potentially clears him to focus attention on the opening at UCLA.
UCLA Director of Athletics Dan Guerrero expressed being "thrilled" at welcoming Kelly to UCLA. "His success speaks for itself, but more than that, I firmly believe that his passion for the game and his innovative approach to coaching student-athletes make him the ideal fit for our program".
Kelly has been named the new coach of UCLA, replacing Jim Mora who was sacked in November.
Chip Kelly's fast-paced offense won't be seen in the Southeastern Conference next season after all.
Kelly went 46-7 in four seasons (2009-12) leading the Ducks, including reaching the BCS championship game after the 2010 season.
The Bruins beat California, 30-27, Friday night under interim coach Jedd Fisch, to qualify for a bowl game appearance this season. He most recently coached the San Francisco 49ers and the Philadelphia Eagles, and led the University of OR to a 46-7 record as head coach from 2009 to 2012.