Kelly also had been considering the vacant Florida job, sources previously told ESPN.
"I am thrilled to welcome Chip Kelly to Westwood," said UCLA director of athletics Dan Guerrero in a statement. "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 perfect fit for our program. 'Champions Made Here' is more than just a mantra at UCLA, and I'm confident that Chip will lead UCLA Football back to competing for championships. I'd like to thank Josh Rebholz, Casey Wasserman and Troy Aikman for their input during this process, as their candor, experience and support were invaluable."
Kelly will be formally introduced as the Bruins' head coach on the UCLA campus on Monday afternoon.
"It is an absolute honor to join the Bruin Family, and I am grateful to Chancellor [Gene] Block and to Dan Guerrero for this incredible opportunity," Kelly said in a statement. "UCLA is a world-class institution with a distinguished history in athletics, and we will do our part to uphold its tradition of excellence."
The Bruins have been looking for a new head coach since Jim Mora was fired Nov. 19, a day after a third straight loss to USC. He had been with the Bruins for six seasons. Offensive coordinator Jedd Fisch was named interim head coach for the remainder of the season.
The Kelly hiring will bring back a well-recognized name to the Pac 12.
Kelly last coached collegiately at Oregon, going 46-7 with the Ducks from 2009 to 2012. Known as an offensive innovator while there, his up-tempo offenses averaged 44.7 points per game during that span. He led Oregon to big bowls in each of his four seasons: the Rose Bowl, BCS title game, Rose Bowl and Fiesta Bowl, respectively.
Kelly left Oregon for the NFL shortly before NCAA sanctions were handed down. He was slapped with "failure to monitor" in the Will Lyles case after he was accused of paying $25,000 to the 7-on-7 coach in exchange for him guiding players to the Ducks. The NCAA ruled that Kelly wasn't aware of Lyles' actions but said he was responsible for ensuring his program was in compliance. Kelly also was handed an 18-month show-cause penalty, which expired in late 2014.
As smooth as his teams in Eugene played, Kelly's two stints as head coach in the NFL were anything but.
Hired by the Eagles in 2013, he went 10-6 in each of his first two seasons in Philadelphia, then was abruptly fired after a 6-9 campaign in 2015. Just weeks later, the San Francisco 49ers hired him, but he lasted just a year there, going 2-14 before being relieved of his duties with three years remaining on his contract.
The 49ers currently owe Kelly approximately $15 million, sources told ESPN's Darren Rovell. What Kelly makes at UCLA will offset that and reduce what the 49ers owe him.
Most recently, Kelly has been serving as an analyst for ESPN. He turned 54 on Saturday.
At UCLA, Kelly will look to stop a disturbing trend in Westwood -- losses to ranked teams. Under Mora, the Bruins dropped six straight games against ranked programs.
The hire itself is a landmark accomplishment for a program that has not won a conference title since 1998 and has not won the Rose Bowl since the 1985 season.
UCLA does currently have the nation's No. 14-ranked recruiting class for 2018 and has finished with a top-20 class the past three years.
Information from ESPN's Kyle Bonagura was used in this report.