Mangini, fired last week by the New York Jets, reached an agreement with the club Wednesday, said the person who spoke on condition of anonymity because Mangini's contract has not been finalized.
Mangini is being represented by agent Ron Shapiro, who is Mangini's father-in-law.
The 37-year-old Mangini began his NFL career as a ballboy with the Browns in 1994.
He went 23-25 and made the playoffs once in three seasons with the Jets, who stumbled down the stretch to lose four of their last five and miss the playoffs after an 8-3 start.
The Browns fired Romeo Crennel after the team went 4-12 this season.