Kelly replaces Bill O'Brien, who was named coach at Boston College earlier Friday. Ohio State had hired O'Brien in mid-January as part of coach Ryan Day's move to no longer call plays and to run the program more holistically.
Kelly and the Buckeyes agreed to a three-year deal. Terms were not disclosed, but Kelly is expected to take a pay cut of more than $4 million with the move, as he made nearly $6 million at UCLA, sources told ESPN.
Additionally, Ohio State will have to pay a $1.5 million buyout for Kelly, sources said.
"We are extremely excited to have Chip and his wife, Jill, joining our program," Day said. "His experience as a head coach at Oregon, UCLA and in the NFL will bring immediate value to our entire team. I am really looking forward to reconnecting with Chip, introducing him to our staff and team and chasing a championship together.
"I would also like to wish coach Bill O'Brien and his family well as he takes over at Boston College."
Earlier Friday, UCLA announced that Kelly was departing the program and a national search for a new head coach had begun.
The reasoning behind Kelly's UCLA departure comes down to an affinity to coach again, spurred in part by coaching UCLA's quarterbacks in the lead-up to the Bruins' bowl game this year. It's the first time in more than a decade Kelly coached a position.
Kelly went 35-34 during six seasons at UCLA, concluding his tenure with three consecutive winning campaigns. He becomes the fourth college coach in this cycle to leave a head-coaching job for an assistant spot, joining Jeff Hafley (Packers), Mo Linguist (Alabama) and Kane Wommack (Alabama).
UCLA athletic director Martin Jarmond said he told the team the plan was to have a new coach in place within four days.
"Timing is a challenge," Jarmond said. "We're looking for a leader, permanently for our program. I told the team to give us 96 hours. Could be earlier, could be later. But we're going to move fast. That's the priority."
Kelly has interviewed for multiple NFL coordinator jobs in the cycle, including most recently the Seattle Seahawks' OC position. He instead stays in college, where he will reunite with Day, his longtime friend and former assistant coach. Kelly has a decades-long relationship with Day, as both are from New Hampshire. Kelly coached Day in college at New Hampshire, and Day worked for Kelly in the NFL with the Philadelphia Eagles and San Francisco 49ers.
Kelly has long been regarded as a gifted playcaller, having served as a longtime offensive coordinator and innovator at New Hampshire and Oregon. As Kelly moved on to become the head coach at Oregon and then in the NFL, he remained the playcaller, and along the way his offenses shifted from breakneck tempo to a more deliberate NFL style.
Ohio State begins spring practice March 5.
Information from The Associated Press was used in this report.