Nugent made seven of nine field-goal attempts in four games this season for the Dallas Cowboys.
The 35-year-old Nugent has made 243 career field goals during a career that began with the New York Jets in 2005. He spent four seasons with Jets, split time with the Arizona Cardinals and Tampa Bay Buccaneers in 2009 and played seven seasons with the Cincinnati Bengals.
Nugent was with the New York Giants during training camp but lost the competition to Aldrick Rosas.
Nugent is expected to play for the Bears (3-9) on Sunday when they visit the Bengals (5-7).