Bradford, 26, was forced to exit Saturday's preseason game against the Cleveland Browns after being struck down by a first-quarter hit from defensive lineman Armonty Bryant.
On Sunday, the Rams said their quarterback would require surgery to repair a torn ACL (anterior cruciate ligament) in his left knee and would miss the entire 2014 season.
"Unfortunately, I can confirm that we have lost Sam for the year," Rams head coach Jeff Fisher told reporters. "For Sam personally, it's devastating."
Fisher was later quoted on the Rams website as saying: "Sam suffered an injury to the reconstructed knee that he had done less than a year ago.
"I met with him this morning. He's left the building to spend time with his parents, and I really can't give you any timetable as to when he's going to have this procedure done.
"Anyone who's gone through that procedure and the rehab understands, to have it happen again within the calendar year is very, very difficult. So we're thinking of Sam."
Bradford had been preparing for his fifth season in the NFL, having missed nine games last season because of an injury to the same knee.
He had completed just 4 of 9 passes for 77 yards on Saturday when he limped off the field. The Rams kick of their regular season against the Minnesota Vikings on Sept. 7.
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