A source said the deal is worth as much as $9 million.
Late Tuesday night the Cowboys agreed to a deal with Doug Free for four years and $32 million, according to sources, and they were able to keep Kosier on Wednesday. Like Free he will not be able to practice until Aug. 4.
Kosier finished a five-year, $15 million deal last season and was scheduled to hit the open market. He had been working out with teammates for most of the offseason and took part in the player-run practices in May even though he was not under contract.
Kosier, who turns 33 in November, is a valuable member of the line because he helps with a lot of the calls before the snap. He missed three games last year with knee and Achilles tendon injuries and was limited to three games in 2008 because of a severe foot injury.
Something of an unknown when he was signed in 2006, Kosier developed into one of the team's more underrated signings. While not the biggest lineman, Kosier uses leverage and athleticism and the Cowboys' running game is better when he is in the lineup.
In April the Cowboys drafted David Arkin in the fourth round with the hopes he could develop into a starter at guard or possibly center in a short time.
The Cowboys could be in the market for a right guard after informing Leonard Davis he will be released. Veteran Montrae Holland is the leading in-house contender for the spot. The club could also part ways with right tackle Marc Colombo, who met with owner and general manager Jerry Jones on Tuesday. If he returns it would be at a lower rate.
Earlier Wednesday, Cowboys reached their first agreement with a draft pick, coming to terms on a four-year deal with seventh-rounder Bill Nagy, a center/guard from Wisconsin.
ESPNDallas.com's Calvin Watkins contributed to this report.
Todd Archer covers the Cowboys for ESPNDallas.com.