NFL Network first reported the move.
Two weeks after Holmes' hire in Detroit, the Rams sent quarterback Jared Goff, along with a 2021 third-round pick and 2022 and 2023 first-round picks, to the Lions in exchange for quarterback Matthew Stafford.
The trades become official at the start of the new league year on Wednesday.
A first-round pick in 2012, Brockers has spent his entire nine-year NFL career with the Rams. He signed a three-year, $24 million contract with the Rams last offseason after a free-agent deal with the Baltimore Ravens fell through.
Brockers could be a salary-cap casualty with the Rams, who were about $33 million over the cap, according to overthecap.com, after the $182.5 million 2021 salary cap was set.
The move will cost the Rams $3.67 million in dead money charges, but it will also produce a cap savings of $6.17 million, according to overthecap.com.
Brockers' $6.5 million base salary becomes fully guaranteed on the fifth day of league year.
But the middle of the line is lacking. The Lions let go of last year's starting nose tackle, Danny Shelton, on Tuesday and have just Nick Williams, Da'Shawn Hand, John Penisini and Kevin Strong under contract at defensive tackle.
The Lions might view Brockers as at least a short-term piece to help the team's defensive reconstruction because he's under contract until 2022. His pass rush win rate (6.5%) and run stop win rate (27%) would be good additions for a Detroit defense that struggled in both areas under former head coach Matt Patricia.
Brockers, who played alongside three-time NFL Defensive Player of the Year Aaron Donald for seven seasons, has 28 career sacks.
ESPN's Michael Rothstein contributed to this report.