Goodson will be called upon to help fill the voids left by veterans Christian Kirksey and Joe Schobert.
Kirksey signed with Green Bay following his release and Schobert has signed with Jacksonville.
“I'm excited about the challenge that's ahead,” Goodson said. “With great challenges comes great responsibility. I'm up for the task and looking forward to getting in and meeting with the staff and learning with my new teammates, getting after it and getting to work.”
Goodson is the third linebacker on the roster, joining second-year players Mack Wilson and Sione Takitaki, both members of Cleveland’s 2019 draft class.
“I want to help lead those guys,” Goodson said. “I feel like I can be a great addition and help for the team.”
Goodson, selected in the fourth round of the 2016 Draft by the Giants, spent last season in Green Bay following a trade from New York prior to the start of the season. He started nine of the 15 games he appeared in for the Packers where he totaled 37 tackles.
Goodson has started 29 of the 52 games he’s appeared in over four seasons registering 160 tackles, seven tackles for loss, three quarterback hits, two forced fumbles and a fumble recovery.
Earlier on Friday, the Browns announced the completion of their trade with Denver for fullback Andy Janovich, who passed his physical. The Broncos received a 2021 seventh-round pick in return.
Cleveland has seven more free agent agreements that are pending physicals and execution of contracts.