General manager Reggie McKenzie announced the deal Friday just hours after Gurode worked out for team officials at training camp.
Gurode has played in 151 games with 127 starts in 10 seasons with Dallas and Baltimore. He was active for two games with Chicago last season but did not see action.
Gurode was selected to the Pro Bowl five consecutive seasons (2006-10) as a member of the Cowboys. He has experience playing both center and guard in the NFL.