The 26-year-old center agreed to terms on a three-year deal worth $16.75 million, including $10 million guaranteed, according to 247Sports' Josh Edwards.
The Packers selected Tretter in the fourth round of the 2013 draft. Since then, injuries have been a dominant theme of his career.
Prior to his rookie season, Tretter broke his ankle and missed the entire year. In 2014, a knee injury limited him to eight games. After playing a full season in 2015, health problems again became a factor for Tretter in 2016, and he missed nine games.
Tretter was one of the league's better centers when he was on the field. Pro Football Focus graded him ninth at his position (84.1) last year. PFF also rated him the best center on the free-agent market, narrowly edging out A.Q. Shipley (82.4).
With the presence of Corey Linsley, the Packers likely feel comfortable letting Tretter leave. Linsley has performed well the last three years, and he has one more year remaining on his current deal.
It's doubtful Green Bay planned on signing both, thus tying up a relatively hefty sum on a nonessential position. Linsley is arguably the better long-term option, since he's a year younger and has less doubt about his durability.
The Packers also have to leave themselves with enough financial flexibility to re-sign offensive guard T.J. Lang.
Signing Tretter makes sense for the Browns. He's an immediate upgrade at center and bolsters the interior of a line that's primed to make a major leap in 2017 following a slew of big free-agent signings.
Performance won't be an issue for for Tretter; the bigger question is whether he can stay on the field for a full season, which could make Cleveland's investment somewhat risky.