Rumors had been running rampant regarding the hiring of former Oregon, Philadelphia Eagles and San Francisco 49ers coach at UCLA.
A big question surrounds Kelly's hiring: Can he replicate his success from OR at UCLA?
UCLA fired Mora last Sunday, a day after a third straight loss to rival USC.
Kelly will be formally introduced in a news conference Monday afternoon on the UCLA campus.
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His stint in San Francisco lasted just one season before he was sacked.
Kelly also had been considering the vacant job with the Florida Gators.
He went 46-7 in four seasons at OR from 2009-2012 before leaving for the National Football League with the Philadelphia Eagles.
While the contract details are not known yet, it's assumed Kelly will be one of the highest-paid coaches in the country and make an annual salary commensurate with that. Mora took the Bruins to the Pac-12 championship game in 2012 and Bowl games in his first four seasons, but they've struggled over the last three campaigns, going 18-19 since 2015.
Kelly, now an analyst at ESPN who turned 54 Saturday, went 46-7 at OR, which averaged 44.7 points a game during that span.