The deal is for one year, ESPN reported.
Moore was expected to be Tony Romo's backup last season before fracturing his fibula in the first week of training camp.
Moore, 27, was put on season-ending injured reserve and Romo injured his back three weeks later in the third preseason game, paving the way for rookie quarterback Dak Prescott to become the starter and lead the Cowboys to a 13-3 season.
Moore appeared in three games (two starts) in 2015 for an injured Romo and completed 61 of 104 passes for 779 yards, four touchdowns and six interceptions.
Moore previously spent three seasons in Detroit (2012-14), including the first two years with Cowboys offensive coordinator Scott Linehan, who then held the same title with the Lions.
The Cowboys are looking to trade the 36-year-old Romo, who is signed through 2019. Dallas intends to release Romo if a trade partner isn't found. Owner Jerry Jones informed Romo recently of the team's plans.
Mark Sanchez, who appeared in one game last season for the Cowboys, remains an unrestricted free agent.
The Cowboys brought in veteran quarterback Josh McCown for a workout two weeks ago and could sign him once they make a move on Romo.