Elam will get $2.5 million for one season, a person familiar with the negotiations tells The Associated Press on condition of anonymity because the team has not announced the deal.
The deal Thursday comes a day after unrestricted free agent safety Gerald Sensabaugh got a similar contract to remain with the Cowboys.
Elam spent the past two seasons in Cleveland playing for new Cowboys defensive coordinator Rob Ryan. Elam started 31 of 32 games while playing for Ryan.
Elam began his NFL career with Dallas in 2006 as primarily a special teams player for 15 games. He then played two seasons with the New York Jets before going to Cleveland.