According to ESPN's Adam Schefter, the deal is worth $80 million and begins in 2019. He was already set to make $8-plus million in 2018.
It was the second time in two years the 24-year-old was traded, having moved from the New Orleans Saints to the Patriots last offseason.
Cooks has been an impact player. The 2014 first-round pick has topped 1,000 receiving yards with at least seven touchdowns in each of the last three years.
In 2017, he averaged a career-high 16.6 yards per catch, which ranked seventh in the league.
However, his contract was a question mark heading into his fifth and final year of his rookie deal, with the team option giving him a salary of nearly $8.5 million in 2018, per Spotrac.
Michael David Smith of Pro Football Talk noted the potential financial problems for the Rams:
Michael David Smith @MichaelDavSmith
Brandin Cooks is in the last year of his contract. So is Aaron Donald. LaMarcus Joyner is on the franchise tag. Suh is on a one-year deal. Talib may no longer be worth his high salary. Gurley's and Peters' salaries skyrocket in 2019. Andrew Whitworth will turn 37 this year.
Still, Los Angeles felt it necessary to extend Cooks.
"Brandin Cooks has shown himself to be a class act on and off the field since the first day he joined our team," Rams head coach Sean McVay said Tuesday. "He's a proven professional in this league, and signing him to a long-term contract was always our goal. We're excited to keep Brandin in a Rams uniform through 2023."
The team is loaded offensively with a young quarterback in 23-year-old Jared Goff, an elite running back in Todd Gurley and an impact wideout in Cooks, all playing for one of the best offensive minds in the NFL, McVay.