The signing comes on the heels of the team adding Mackenzy Bernadeau to a four-year, $11 million deal Wednesday, and should complete the moves on the interior of the offensive line.
Livings, who visited with the Cowboys Thursday before taking a trip to St. Louis, started 32 straight games in Cincinnati the past two years and 47 in the past four years. He turns 30 later this month.
He is the Cowboys' seventh signing of the free-agency period, joining cornerback Brandon Carr, quarterback Kyle Orton, safety Brodney Pool, fullback Lawrence Vickers, linebacker Dan Connor and Bernadeau.
Livings' arrival was bad news for Kyle Kosier, a starter since arriving in 2006 via free agency. The Cowboys released Kosier Friday, according to league sources.
Kosier had started 80 straight games in which he was active since joining the Cowboys as a free agent in 2006. He signed a three-year deal last summer after the lockout ended and started every game.
The move would save the Cowboys $1.55 million in salary cap space and continue the overhaul of the offensive line. Right tackle Doug Free is now the longest-tenured offensive linemen having joined the team in 2007. The second-longest tenured is center Phil Costa, who joined the team as an undrafted free agent in 2010.
Kosier earned a $1 million escalator that would have jumped his base salary in 2012 to $2.25 million. In the last two seasons the Cowboys have parted ways with Andre Gurode, Marc Colombo and Leonard Davis, mainstays on the lines for years.
The Cowboys also re-signed wide receiver Kevin Ogletree on Friday.
Ogletree, a New York native, visited the New York Giants Wednesday. It's a surprise in some ways considering Ogletree lost the No. 3 receiver spot to Laurent Robinson last year and didn't play in regular-season finale despite being active.
Information from ESPNDallas.com's Dallas Watkins was used in this report.