Cox, 34, is a four-time Pro Bowl player who became the first long-snapper named to an All-Pro team this year. He had been with Baltimore since he went undrafted in 2010.
"It's almost the circle of life at times, and you have to continue to get younger as a team," general manager Eric DeCosta said Monday. "Although it was very, very difficult to move on from Morgan, it was probably something we needed to do long-term. Things change. Unfortunately, it's a tough part of this business."
The Ravens are turning to Nick Moore, a former XFL long-snapper who was on the Ravens' practice squad all last season. Moore is six years younger than Cox and less expensive. Cox earned $1.1 million last season.
Cox's 165 games played in Baltimore ranks seventh all-time in Ravens history.