Leary will fly to Denver on Friday to sign the deal, which includes $20 million guaranteed. He's expected to slide in at left guard with Max Garcia moving over to battle it out with Michael Schofield on the right side.
Playing alongside All-Pro offensive linemen Tyron Smith, Travis Frederick and Zack Martin with the Cowboys, Leary received little notice and lost his job -- through no fault of his own -- in 2015 to La'el Collins, who received a fully guaranteed deal as an undrafted free agent after a heavy recruiting process by owner and general manager Jerry Jones.
In 2012, the Cowboys signed Leary as an undrafted free agent to a deal that included more than $200,000 guaranteed. He fell off the draft boards because of a knee condition that never proved to be an issue with the Cowboys.
After spending the 2012 season on the Cowboys' practice squad, Leary started 31 of 32 games at left guard over the next two seasons. He helped DeMarco Murray to a franchise-record 1,845 rushing yards in 2014 and opened the 2015 season as the starter but suffered a groin injury and eventually lost the job to Collins.
The Cowboys gave him a second-round tender as a restricted free agent in 2016 and had some trade discussions during the draft and in training camp, but they opted to keep him. When Collins suffered a season-ending toe injury in Week 3, Leary stepped in and helped Ezekiel Elliott to the NFL rushing crown with 1,631 yards.
Leary, who turns 28 on April 29, has started 47 games in his career, as well as three playoff games.
ESPN's Todd Archer and The Associated Press contributed to this report.