A person with knowledge of the deal told The Associated Press that the team was working on final details of the contract Tuesday night. The person spoke on condition of anonymity because an agreement had not been announced.
Melton missed most of last season with Chicago after tearing a ligament in his left knee against Pittsburgh on Sept. 22. He will be reunited with former Bears defensive coordinator Rod Marinelli, who now has the same title in Dallas.
The fifth-year player was a high school running back in the Dallas area before becoming a defensive tackle with the Texas Longhorns.
The 27-year-old Melton has 15 1/2 sacks and 63 tackles in 48 career games, including 32 starts. The Bears drafted him in the fifth round in 2009, and he missed his rookie season with an ankle injury.
Melton was arrested in December in Grapevine, where he went to high school, on charges of assault and public intoxication after police say he refused to leave a bar and fought with employees.
Police say Melton was accused of punching the bar manager in the face and biting his arm. Melton's agent, Jordan Woy, said at the time that his client didn't start the altercation.
The Cowboys released Ware, their star defensive end, just as free agency opened. Defensive tackle Jason Hatcher signed with Washington after leading the Cowboys with 11 sacks last season.
A day after Ware's release, the Cowboys signed defensive end Jeremy Mincey and defensive tackle Terrell McClain. Mincey is the team's current career leader with 20 sacks, now followed by Melton.
Next on this list with 10 is George Selvie, who wasn't even on the Dallas roster when training camp started last season and ended up second to Hatcher with seven sacks on an injury plagued unit.
Marinelli came to Dallas a year ago as defensive line coach with then-defensive coordinator Monte Kiffin after Lovie Smith was fired in Chicago. He was promoted when Kiffin was reassigned after the Cowboys gave up the most yards in franchise history and finished last in the NFL in total defense.
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