Bradford is the centerpiece of a rebuilding effort for the Rams, who were 1-15 last year in the first season under coach Steve Spagnuolo and are 6-42 the last three seasons.
Spagnuolo reiterated earlier this week that veteran backup Jay Feeley is the starter entering training camp. But Bradford, the 2008 Heisman Trophy winner, shouldn't be on the bench for long.
Marc Bulger, rookie Keith Null and Kyle Boller combined for only 12 touchdown passes all last year. St. Louis trailed the NFL with a 10.9-point scoring average, leaning heavily on Pro Bowl running back Steven Jackson.
Quarterback Matthew Stafford, the No. 1 pick last year, got $41.7 million in guaranteed money on a six-year, $72 million deal with the Lions last year.
Bradford's agents, Tom Condon and Ben Dogra of St. Louis, also represent Rams offensive tackle Jason Smith and Smith also signed just in time for the first full-squad workout. Smith was the second overall pick last year and got a five-year, $62 million deal with $33 million in guaranteed money.
Bradford led the nation with 48 touchdown passes in 2008. He played in only three games in 2009 before undergoing season-ending shoulder surgery.
Bradford attended the team's mandatory minicamp last month as well as a rookie minicamp after the draft. He missed three practices for rookies, quarterbacks and veterans coming off injuries, two of them on Thursday.