The reports by the Seattle Times, ESPN and the Los Angeles Times said Carroll, 58, a former NFL coach with the New York Jets and the New England Patriots, will end his nine-year tenure with the Trojans by Monday.
The LA Times said Carroll would get a five-year contract worth $7 million per year.
Some had expected him to serve as team president as well, but he won't hold that post.
Carroll's career record in the NFL is 33-31 in the regular season and 1-2 in the playoffs.
His program at USC has come under fire recently due to investigations into possible NCAA rules violations.
Star running back Joe McKnight missed the Emerald Bowl after an LA Times report said he was spotted driving a Land Rover owned by Santa Monica businessman Scott Schenter, who reportedly has ties to marketing interests or agents.