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, 26, 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.
ESPN's Adam Teicher contributed to this report.