ESPN.com's John Clayton reported that the deal is for one year at $3 million.
Saturday night, Thomas' agent, Drew Rosenhaus confirmed the deal.
"It is going to be signed in the next couple of days,"
Rosenhaus was quoted as saying by The Associated Press.
The deal includes a $1 million base salary, a $1 million signing
bonus and a $1 million incentive-based bonus based on playing time
that Rosenhaus said should be easily attained.
Thomas, 34, who was released by the Miami Dolphins two weeks ago, following a 2007 season in which he was limited to just five appearances, chose the deal from the Cowboys over contract proposals from the New England Patriots and the New Orleans Saints.
A 12-year veteran, and one of only three players in modern NFL history to register 100-plus tackles in each of his first 10 seasons in the league, Thomas was released by the new Miami football regime on Feb. 14 after a celebrated stint with the Dolphins.
He suffered a concussion early last season, was plagued by headaches for much of the year, and finally placed on injured reserve in early December, culminating what was easily the least productive campaign of his career.
While none of the teams that met with Thomas following his release publicly addressed the residual effects of his 2007 concussion, all three made contract offers -- seemingly indicating confidence in his medical readiness to play in 2008.
Thomas had originally planned to fly to Dallas and Houston next week to meet with those teams. But he decided to fly into Indianapolis and meet with the Cowboys Friday. The meeting went well enough for Thomas to reach an agreement Saturday afternoon.
Thomas grew up in Pampa, Texas and played college football at Texas Tech.
A fifth-round pick in the 1996 draft, Thomas led the Dolphins in tackles in 10 of his 12 seasons with the team. The former Texas Tech star posted 100 or more tackles in all but one season.
For his career, Thomas, who will play inside in the Cowboys' 3-4 front, has 1,642 tackles, 19½ sacks, 17 interceptions, 65 passes defensed and 15 forced fumbles.
Len Pasquarelli is a senior NFL writer for ESPN.com. Information from The Associated Press and ESPN.com senior NFL writer John Clayton was used in this report.