"Jason is an established leader who has started a number of games in this league and has had success," Browns coach Rob Chudzinski said in a team statement. "He brings us a veteran presence and a good set of physical tools. He played in a similar system when he was in Oakland and that will help in his transition."
Campbell, a first-round pick by Washington in 2005, has started 77 games and thrown 76 touchdowns during his NFL career. He played his first five seasons with the Redskins before he was traded to Oakland in 2010. Campbell spent two seasons with the Raiders.
He went 4-2 in his first six games as Oakland's starter in 2011 before sustaining a broken collarbone that ended his season. He signed with Chicago as an unrestricted free agent in 2012 and made one start.
The Browns have been looking for a QB to bring in and push Weeden, who had an uneven rookie season. Campbell could challenge Weeden for the starting job.
Information from The Associated Press was used in this report.