The person spoke to The Associated Press on the condition of anonymity because the team had not yet announced the move.
Orton finished last season in Kansas City after being released by Denver.
Jon Kitna, Romo’s backup the last two years, retired after last season. The 39-year-old Kitna appeared in only three games last year after starting the final 10 games in 2010 when Romo broke his collarbone.
After Kitna injured his back last fall, the Cowboys unsuccessfully tried to claim Orton off waivers following his release by the Broncos.