The deal is for $48 million and includes $30 million guaranteed, per reports.
The Chiefs were not done, however, as they also are expected to sign free-agent linebacker Anthony Hitchens, multiple outlets reported.
Watkins led Los Angeles with eight receiving touchdowns despite reeling in just 39 catches for 593 yards. He had three or fewer catches in 12 of 15 games this past season for the Rams, who elected to place the non-exclusive franchise tag last week on safety Lamarcus Joyner.
The 24-year-old Watkins was selected by the Buffalo Bills with the fourth overall pick of the 2014 NFL Draft. He recorded 125 catches for 2,029 yards and 15 touchdowns in his first two seasons (29 games), but a broken bone in his foot caused him to miss the first eight contests of the 2016 campaign.
The Bills traded Watkins to the Rams in exchange for cornerback E.J. Gaines and a 2018 second-round pick on Aug. 11.
Watkins will join Tyreek Hill and tight end Travis Kelce in a new-look offense that will feature quarterback Patrick Mahomes, who takes over for the departed Alex Smith.
Hitchens recorded 84 tackles and a forced fumble in 12 starts with the Dallas Cowboys last season after missing the first four games with a knee injury.
The 25-year-old has collected 304 tackles, 3.5 sacks and one interception since being selected by the Cowboys in the fourth round of the 2014 NFL Draft.
Hitchens joins a Kansas City rush defense that permitted 118.1 yards per game, which ranked 25th in the league.