Floyd, a first-round pick in 2016, was released by the Chicago Bears on Tuesday.
Los Angeles is in the midst of retooling its defense ahead of the 2020 campaign. Free agents Cory Littleton, Michael Brockers, and Dante Fowler signed with new teams, while safety Eric Weddle announced his retirement.
After recording seven sacks as a rookie, Floyd accumulated just 11.5 over the last three seasons. He's started all 54 games of his career and performed well in run defense.