Coach Steve Spagnuolo said in a release that it was difficult to make the move and wished the 33-year-old Bulger well. Last month the Rams signed A.J. Feeley, presumably as next year's backup on a team that was 1-15 in 2009.
"It is always hard to part ways with someone you care for and appreciate," Spagnuolo said. "I will always be indebted to him for his work ethic, character and leadership."
The Rams were among the teams impressed by Bradford's workout last week in Norman, Okla. Bradford, the 2008 Heisman Trophy winner, made a convincing case that he would make a complete recovery from shoulder surgery last October, completing all but one of 50 passes.
Bulger started eight games last season, but was sidelined the last six with a fractured left shin bone, finishing the year on injured reserve. Rookie Keith Null started the last four games, and veteran Kyle Boller also made four starts.
Bulger made 95 starts for St. Louis starting in 2002 and took the starting job from Kurt Warner in 2003, leading the Rams to a 12-4 record. He went to the Pro Bowl in 2004 and 2006, throwing for more than 4,000 yards in '06, but has been plagued by injuries in recent seasons.
In nine seasons, all with the Rams, he completed 62.1 percent of his passes for 22,814 yards, with 122 touchdowns and 93 interceptions. He signed a six-year, $65 million contract in training camp in 2007.
Bulger was scheduled to make $8.5 million this season.
Information from The Associated Press was used in this report.