Mora and UConn have agreed to a five-year contract in which he will make $1.5 million in the first season and could earn another $200,000 in annual performance incentives.
Mora, who is 59, last coached in 2017, his final season at UCLA.
Edsall went 6-32 in his second stint as Huskies coach after guiding the program to two Big East titles and a Fiesta Bowl appearance during his first run from 1999 to 2010.
“Jim is a proven winner, a man of integrity, and he possesses the experience and the energy to lead our football program back to success,” Benedict said in a statement.