Bailey, who went undrafted out of Oklahoma State in 2011, played seven full seasons with Dallas. The 30-year-old has connected on 88.2% of his career field-goal attempts, marking the second-most accurate figure in NFL history.
Last season, Bailey made 15-of-20 field-goal attempts, appearing in 12 games while dealing with back and groin injuries.
Bailey was owed a base salary of $3.4 million each of the next three seasons, according to Dallas Morning News' Brandon George. In 2014, Bailey had signed a seven-year, $22.5 million contract.
The Cowboys retained the services of kicker Brett Maher. In April, Dallas signed Maher, who had spent most of his professional career in the Canadian Football League after going undrafted out of Nebraska in 2013. Maher had a brief stint with the Cleveland Browns last season, but did not appear in a game.
Maher also doubles as a punter. Maher kicked only two field goals this preseason, both during the Cowboys' finale. He made each attempt, hitting from 57 and 41 yards out.