The hiring is expected to be announced by the school Saturday, with an introductory news conference to come sometime next week.
The position will be Mora's first at the collegiate level since serving as a defensive assistant in 1984 at Washington, where he also played defensive back. Mora was born in Los Angeles, and his father, Jim E. Mora, was an assistant coach at UCLA in 1974.
Mora will be the first UCLA coach since 1949 to have neither worked as an assistant nor played at the school. He will succeed Rick Neuheisel, who was fired before UCLA's loss to Oregon in the Pacific-12 Conference championship game. Neuheisel had a 21-29 record in four years at the school.