Nugent, Jason Myers and Sam Irwin-Hill all worked out for the Cowboys on Tuesday before Dallas opted for Nugent. Irwin-Hill was cut by the Cowboys during the preseason, while Myers was recently released by the Jacksonville Jaguars.
The 35-year-old Nugent has made 236 career field goals during a 12-year-career that began with the New York Jets in 2005. He spent four seasons with Jets, split time with Arizona and Tampa Bay in 2009 before spending seven seasons with the Cincinnati Bengals.
Nugent was with the New York Giants during training camp but lost the competition to Aldrick Rosas.
The injured Bailey is the most accurate kicker in NFL history at 89.9 percent, having made 178 of 198 field-goal attempts. He has been the Cowboys' kicker since 2011.
Dallas released defensive end Damontre' Moore to open a roster spot. Moore had five tackles in three games and was inactive against the 49ers.