Details of the trade, which won't be processed until the start of the new league year on March 14, have yet to be disclosed. But the Chiefs are expected to receive a package of draft picks, not players, in return, according to Schefter's sources.
Peters steps in as the Rams' primary cornerback, which might spell the end of Trumaine Johnson's tenure with the team. Peters, a two-time Pro Bowler who was named first-team All-Pro in 2016, has compiled an NFL-leading 19 interceptions since being drafted 18th overall three years ago.
The 25-year-old will cost $1.74 million toward the salary cap this season, which is nearly one-tenth of Johnson's cap hit last year. The Rams would then have until May 3 to pick up Peters' fifth-year option for 2019.
The Rams entered the offseason with a desperate need at cornerback. Johnson, who spent the past two years playing under the franchise tag, and slot corner Nickell Robey-Coleman are scheduled to be unrestricted free agents. Their No. 2 cornerback, Kayvon Webster, ruptured an Achilles tendon in December. Beyond them, there isn't much depth.
The Peters acquisition gives the Rams salary-cap flexibility, which they could use on pending free agents such as safety Lamarcus Joyner and wide receiver Sammy Watkins. It also helps them sign defensive tackle Aaron Donald to an extension that is expected to eventually make him the game's highest-paid defensive player.
Just as important, it provides a shutdown corner for defensive coordinator Wade Phillips.
Peters is the first player since Ed Reed (from 2002 to 2004) with five interceptions in each of his first three seasons, even though opposing quarterbacks have continually shied away from him. From 2015 to 2017, Peters' combination of sacks, forced fumbles and interceptions (25) easily led the NFL, according to ESPN Stats & Info.
But Peters also joins the Rams with some character concerns. He was thrown off his collegiate team at Washington for an altercation with an assistant coach. In December, he was suspended by the Chiefs for one game after tossing an official's penalty flag into the crowd and then retreating to the locker room without being ejected during a game against the New York Jets.
Peters was also seen at different times on the sideline last season shouting at defensive coordinator Bob Sutton or others. In at least one instance, he directed expletives at a group of fans behind the Chiefs' bench. The Rams are hopeful that a change of scenery can help fix that.
ESPN's Adam Teicher contributed to this report.