The source said Watkins' new deal has a maximum value of $16 million, including $7 million in incentives, and contains a no-trade clause.
The move creates $5 million in salary-cap space for the Chiefs, according to Yahoo Sports, which first reported the restructured contract.
The Super Bowl champions were down to $171 in cap space prior to the new agreement.
Watkins acknowledged the move on Twitter on Friday morning, writing "Im back KC LETS GET IT..! #RUNITBACKTOUR"
Im back KC LETS GET IT..! #RUNITBACKTOUR— King me (@sammywatkins) April 3, 2020
The move keeps the Chiefs' top four receivers from 2019 -- Watkins, Tyreek Hill, Demarcus Robinson and Mecole Hardman -- together for next season. Kansas City signed Robinson to a one-year contract last month.
Watkins had been scheduled to make $13.7 million in base salary in 2020 and count a prohibitive $21 million against the cap.
The 26-year-old Watkins has been mainly a third receiving option for the Chiefs, and other than the occasional big game -- most notably a 198-yard, three-touchdown showing against the Jacksonville Jaguars in the 2019 regular-season opener -- he hasn't produced a lot for Kansas City in two seasons. He has caught 92 passes for six touchdowns in 24 regular-season games.
But Watkins delivered in each of the past two AFC Championship Games, with 100-plus receiving yards in both contests. His 38-yard catch was the big play on the Chiefs' go-ahead touchdown drive in the fourth quarter of Super Bowl LIV, and general manager Brett Veach has said the Chiefs signed Watkins for the big games.
"He's done a great job for us," Chiefs coach Andy Reid said Thursday, before news of the reworked deal came out. "And as good a player he is, he's an even better person, so we've enjoyed having him here."
ESPN's Adam Teicher and The Associated Press contributed to this report.