A source told ESPN that the deal is worth $80 million.
Los Angeles announced the deal on Tuesday afternoon. Cooks, 24, joined the team in April as part of a trade from the New England Patriots. The Patriots sent Cooks and a 2018 fourth-round NFL Draft pick to the Rams in exchange for 2018 first and sixth-round draft picks.
"Brandin Cooks has shown himself to be a class act on and off the field since the first day he joined our team," Rams coach Sean McVay said in a news release.
"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."
Cooks was the No. 20 overall pick in the 2014 NFL Draft out of Oregon State. The 5-foot-10, 183-pound pass catcher had 1,082 yards and seven touchdowns on 65 receptions in 16 games in 2017. He had a career-best 1,173 yards and eight scores on 78 receptions in 16 games during the 2016 season with the Saints. Cooks had career-highs in receptions (84) and touchdowns (9) during his sophomore season in New Orleans.