Rivers was cut by the Buffalo Bills on Feb. 17 after signing a two-year deal worth $5 million with the club in 2014. He started three games last season and played in 12 but recorded just 16 tackles as his playing time decreased dramatically late in the year.
The Cowboys have three free-agent linebackers in Rolando McClain, Justin Durant and Bruce Carter. While the signing does not preclude any from coming back it might affect Carter the most because Rivers is a strong-side linebacker.
The Cowboys have had discussions with the agents for McClain and Durant about returning but both could test the market when it opens next week
Rivers, who turns 29 in May, was a first-round pick of the Cincinnati Bengals in 2008 and spent two years with the New York Giants (2012-13) before joining the Bills. For his career he has 291 tackles, three sacks and two interceptions.