The deal is worth $48 million with $30 million guaranteed, sources told ESPN's Dianna Russini.
Free-agent linebacker Anthony Hitchens will also sign with the Chiefs, according to ESPN and multiple reports.
Watkins, 24, proved he could stay healthy while with the Rams in 2017, but his numbers didn't stack up among the game's best receivers. Acquired from the Buffalo Bills in August, Watkins finished with only 39 catches for 593 yards, though he did manage to score eight touchdowns.
The big, physical receiver (6-foot-1, 211 pounds) specializes in stretching defenses vertically. With the Rams, though, that mostly benefited the likes of Robert Woods, Cooper Kupp and Todd Gurley underneath.
Watkins entered the NFL with the promise of being one of the game's best receivers. He starred at Clemson, and the Bills gave up future first- and fourth-round picks to move up five spots and draft him at No. 4 overall in 2014.
He showed glimpses of star potential in his first two seasons, totaling 125 catches for 2,029 yards and 15 touchdowns in 29 games. But a broken bone in his left foot eventually forced him to miss the first eight games of the 2016 season, prompting the Bills to decline their fifth-year option. Buffalo sent Watkins to the Rams on Aug. 11 in exchange for cornerback E.J. Gaines and a 2018 second-round pick.
Watkins previously underwent two surgical procedures on his foot and had hip surgery after the 2014 season.
A fourth-round pick in 2014, Hitchens started 48 of 60 games in his four seasons with the Dallas Cowboys, playing weakside, middle and strongside linebacker in their 4-3 scheme.
Hitchens had 84 tackles in 12 starts in 2017. He missed the first four games of the season with a knee injury suffered in the preseason.
In addition, Hitchens, who turns 26 in June, had two pass deflections and a forced fumble and was credited by Cowboys coaches with nine tackles for loss and five quarterback pressures in 2017.
At 6-foot, 235 pounds, he is not the biggest linebacker, but his coaches raved about his instinctiveness, which was aided by the presence of Sean Lee. Hitchens' ability to play all three linebacker spots helped the Cowboys deal with injuries to Lee and Jaylon Smith.
ESPN's Alden Gonzalez and Todd Archer contributed to this report.