The Browns released Young on Tuesday.
Young, who turns 28 in May, intercepted a career-best three passes for Cleveland last season. He made starts at both safety spots in his two seasons with the Browns.
The Bengals do not have a clear-cut starter at strong safety. Chris Crocker, who finished the season with the job, is an unrestricted free agent.
Young (6-0, 200) began his NFL career in New Orleans (2007-2010). He played collegiately at Kent State.