As part of the deal, which was officially announced by the Rams on Tuesday night, New England also sent a fourth-round pick (No. 136 overall) to Los Angeles and received a sixth-round pick (No. 198 overall) from the Rams.
The Patriots attempted to re-sign Cooks before talks broke off, and the Rams now will continue those talks with the intent to sign Cooks to a long-term deal, sources told ESPN's Adam Schefter.
The deal helps both teams in different ways.
The Rams -- who had explored a trade for Odell Beckham Jr. but liked the Cooks option better -- were seeking a vertical threat for second-year coach Sean McVay's dynamic offense after Sammy Watkins joined the Kansas City Chiefs in free agency.
The speedy Cooks, who totaled 65 receptions for 1,082 yards and seven touchdowns for the Patriots last season, fills that void alongside Robert Woods and Cooper Kupp. Cooks had 16 receptions on passes thrown 20-plus yards downfield last season, tied with DeAndre Hopkins for most in the NFL.
Cooks had made a strong impression on many in New England after the team acquired him last offseason from the New Orleans Saints for a package that included the Patriots' first-round pick (No. 32 overall), but he was entering the final year of his contract (due to earn $8.459 million) at a time when salaries for top pass-catchers have skyrocketed.
By trading Cooks, the Patriots accumulated assets at a time when quarterback Tom Brady turns 41 in August and tight end Rob Gronkowski appears to be on a year-to-year plan in terms of how much longer he will play.
The Patriots, who hope to sustain success as some of their star players enter the final stages of their careers, now have two first-round picks (No. 23, 31) and two second-rounders (No. 43, 63), along with a third-rounder (95), two sixth-rounders and a seventh-rounder this year.
As for their wide receiver depth chart, it is still well stocked with Julian Edelman, Chris Hogan, Phillip Dorsett, Malcolm Mitchell, Kenny Britt, Cordarrelle Patterson, Riley McCarron and Cody Hollister, although the club will miss Cooks' blazing speed and durability, as he played 92.7 percent of the offensive snaps in the regular season and coach Bill Belichick said he never missed a practice.
Cooks had 10 catches for 155 yards in the postseason before being knocked out of the team's Super Bowl LII loss to the Philadelphia Eagles with a concussion in the second quarter.
The 24-year-old Cooks, who entered the NFL as a first-round draft choice of the Saints in 2014, is the latest star acquisition for the Rams this offseason. They previously traded for cornerbacks Marcus Peters and Aqib Talib, then signed defensive tackle Ndamukong Suh, whom they will introduce to the media Wednesday.
Several current Rams players took to Twitter to cheer the move.
Aw man the front office is out here cookin! 👀👨🏾🍳 #Rams— Rodger Saffold (@Rodger_Saffold) April 3, 2018
The Rams will be without a first-round pick for the second consecutive year. They were hoping to use this year's pick to help address drastic needs at linebacker.
The 23rd overall pick will be the Patriots' highest in the draft since 2012, when they selected Chandler Jones 21st overall. In addition, they now have two first-round picks in the same draft for the third time under Belichick. In 2012, they selected Jones and Dont'a Hightower. In 2004, they took Vince Wilfork and Benjamin Watson.
ESPN Rams reporter Alden Gonzalez contributed to this report.