The Rams will get Cooks and a fourth-round draft pick from the Patriots, while New England will receive the 23rd overall pick in the first round of this year's draft as well as a sixth-round draft pick from the Rams.
Acquiring Cooks probably means the Rams have given up on attempts to obtain Odell Beckham Jr. from the New York Giants. The New York Post reported the Rams had been the front-runners for Beckham before this trade.
New England had acquired Cooks from the New Orleans Saints in a March 2017 trade that sent the Patriots' first-round pick (No. 32 overall) to the Saints.
Cooks had 65 catches for 1,082 yards and seven touchdowns in his only season with the Patriots. He added 10 catches for 155 yards in the Patriots' three postseason games.
Cooks had one catch in the Super Bowl LII loss to the Philadelphia Eagles before he left the game with a concussion.
Last season, Cooks had 16 receptions on passes thrown 20 yards or more downfield. That tied DeAndre Hopkins for the most such receptions in the NFL.
The Rams now have no first-round picks in the upcoming draft.
The 23rd overall pick will be the Patriots' highest in the draft since 2012, when they selected Chandler Jones 21st overall.