The Rams and the former Oklahoma quarterback concluded negotiations in time for the first full-squad workout, set for Saturday. The guaranteed money is the highest ever in the NFL.
Sources told ESPN that the deal can be worth as much as $86 million.
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 past three seasons. The Rams have not made the playoffs since making five postseason appearances from 1999 to 2004.
Spagnuolo reiterated earlier this week that veteran backup A.J. 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.
Spagnuolo said after Friday morning's practice that he didn't think Bradford had fallen too far behind.
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 last year Smith also signed just in time for the first full-squad workout. Smith was the second overall pick in 2009 and got a five-year, $62 million deal with $33 million in guaranteed money.
The Rams made Bradford the top selection in April's draft despite Bradford missing the majority of the 2009 season at Oklahoma with a right shoulder injury that eventually required surgery.
In 2008, as a redshirt sophomore, Bradford threw for 4,721 yards and 50 TDs with just eight interceptions. That year, he beat out fellow 2010 draft picks Colt McCoy and Tim Tebow to win the Heisman Trophy.
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.
Information from ESPN NFL Insider Adam Schefter, ESPN.com NFL Insider Chris Mortensen and The Associated Press contributed to this report.