Rapoport added Watkins is slated to make "roughly $16 million per year over three years."
Watkins will be eligible to finalize his agreement with the Chiefs when free agency officially opens Wednesday.
The Los Angeles Rams acquired Watkins in an August trade with the Buffalo Bills, who selected him with the fourth overall pick in the 2014 NFL draft, in exchange for cornerback E.J. Gaines and a 2018 second-rounder.
The 24-year-old Clemson product failed to make a major impact despite the passing game's overall improvement, reeling in just 39 catches across 15 games. His per-catch average (15.2 yards) ranked 15th in the league, however, and he also produced eight touchdowns.
In October, the big-play weapon explained how his mindset had changed since his time in Buffalo, when he often lamented his lack of involvement.
"Two years ago, it would've probably been different," Watkins told reporters. "I would've probably gone to the media and been saying whatever, trying to get the coach's attention. That's how I used to do it back then. Like, 'I need more targets.' Then that comes to the coach, and me and him have to talk."
He added: "We have too many great guys that need their touches. So for me, it's really just focus on blocking, focus on getting open, focus on showing coach [Sean McVay] that I can play without the ball, that I'm not selfish."
Watkins tallied 153 receptions for 2,459 yards and 17 touchdowns in 37 appearances during his three years with the Bills.
Along with failing to reach the expectations associated with a top-five selection, he also dealt with lingering foot problems that caused him to miss games and frequently limited his on-field effectiveness. That, in part, likely prevented a franchise tag or long-term contract.
That said, the Florida native managed to avoid any further injury-related setbacks throughout his first season in L.A. His only absence came in Week 17 when the Rams rested their starters with a playoff berth already secure.
As Watkins joins the Chiefs, look for him to slot in as a starter across from Tyreek Hill, forming what could be one of the NFL's most dynamic receiving duos. New Chiefs starting quarterback Patrick Mahomes II has a big arm, and Watkins should mesh perfectly with that skill set.