The Browns lost linebackers Christian Kirksey and Joe Schobert earlier in the week. They added a linebacker Wednesday.
B.J. Goodson agreed to terms with the Browns, NFL Media reports.
Goodson, 26, spent last season in Green Bay. He played 15 games with nine starts, seeing action on 254 snaps on defense and 145 on special teams.
He made 37 tackles last season.
The Giants made Goodson a fourth-round choice in 2016, and he spent his first three seasons in New York.
In 52 career games, with 29 starts, Goodson has made 160 tackles, seven tackles for loss, two interceptions, two forced fumbles and six pass breakups.