Mangini, fired last week by the Jets, agreed to a four-year deal, a source close to the situation told ESPN.com's Michael Smith on Wednesday.
A person with knowledge of the negotiations told The Associated Press that Mangini will be introduced Thursday at a news conference at the team's headquarters in Berea.
Mangini began his NFL career as a ballboy with the Browns in 1994 under then-coach Bill Belichick. Now he's taking over the job of one of his best friends in football, fired Browns coach Romeo Crennel.
Mangini 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 games and miss the playoffs after an 8-3 start.
His tenure in New York was tumultuous. When he arrived, Mangini inherited a 4-12 Jets team and led them to 10 wins in his first season, prompting New York's tabloids to dub him "Mangenius." By the end of his run in the NFL's largest market, he was being called moody, dour and controlling.
Mangini took the fall after the Jets finished a disastrous stretch in which they lost to Denver, San Francisco and Seattle -- three non-playoff teams -- in the final month behind 39-year-old quarterback Brett Favre's injured arm and questionable play calling by Mangini.
Mangini and Crennel both lost their jobs on Dec. 29, although Browns owner Randy Lerner was not aware of Mangini's dismissal when he met with the media regarding Crennel.
Lerner wasted no time in going after Mangini and interviewed him the following night in the New York area.
Despite the Jets' meltdown, Lerner was enamored with Mangini's potential and believed he would bring discipline to the underachieving Browns. Lerner also believed Mangini, who will be 38 on Jan. 19, learned from his mistakes in New York.
Jets running back Leon Washington said in an e-mail to The Associated Press that he was pleased to see Mangini land another head coaching job.
"I am really happy for Coach Mangini," Washington said in the e-mail. "I learned so much from him while he had his tenure with the Jets. His hardworking, selfless and competitive approach really helped me. ... The Browns got themselves a really good coach."
Jets long-snapper James Dearth said the Browns are a good fit for Mangini. "They run the same type of defense there, so they already have the right personnel for him. I hope he does well there," Dearth said.
Mangini will hire Jets quarterbacks coach Brian Daboll, whose contract is expiring, as his offensive coordinator, league sources told Smith.
For the position of defensive coordinator, sources told Smith that Mangini will bring aboard Raiders defensive coordinator Rob Ryan, whose contract with Oakland is up. Sources also said that Mangini and Crennel discussed the possibility of Crennel's returning to work with Mangini but decided it best to both go in a different direction.
Mangini and Crennel became friends during their days as assistants with the Jets under Bill Parcells. Mangini was a defensive assistant while Crennel was the defensive line coach from 1997 to 1999. Mangini followed Belichick to New England in 2000, and Crennel joined the Patriots' staff a year later after a stint as Cleveland's defensive coordinator.
Crennel and his wife, Rosemary, stayed with Mangini and his wife, Julie, for about six months when the Crennels were having a home built after Romeo took the job as New England's defensive coordinator.
When Crennel was hired as Cleveland's coach, he wanted Mangini as his defensive coordinator, but Mangini decided to take over Crennel's spot with the Patriots instead.
Mangini was one of four candidates interviewed by Lerner, but the only one with NFL head coaching experience -- a prerequisite for the Browns owner, who also spoke with New York Giants defensive coordinator Steve Spagnuolo, New England offensive coordinator Josh McDaniels and Browns defensive coordinator Mel Tucker.
Mangini takes over a Browns team with more talent than Crennel had when he arrived in 2005. Cleveland entered 2008 with high expectations after going 10-6 last year. But beginning with a training camp injury to wide receiver Braylon Edwards, who cut his foot while running in his socks after practice, the season unraveled quickly.
The Browns blew back-to-back home games in a five-day span and finished the season 4-12 without scoring an offensive touchdown in their final six games. On the way to their fifth season of at least 10 losses in the past six years, the Browns changed quarterbacks, benching Pro Bowler Derek Anderson in favor of Brady Quinn.
Lerner fired GM Phil Savage after a 31-0 loss at Pittsburgh in the season finale. He then interviewed Scott Pioli, New England's highly regarded director of player personnel, and had hoped to pair him with Mangini in Cleveland. The two began their pro careers together with the Browns, but their relationship may have been strained when Mangini reported the Patriots to the NFL for videotaping New York's defensive signals during a game.
During his interview, Mangini mentioned Baltimore player personnel director George Kokinis as his preference as GM. Kokinis is expected to interview with Lerner on Sunday.
Information from ESPN.com's Michael Smith and The Associated Press was used in this report.