After using the exclusive franchise tag on their quarterback earlier Monday, the Cowboys reached agreement on a new deal with Cooper.
The Pro Bowl receiver will sign a five-year, $100 million contract, Adam Schefter of ESPN reports.
Cooper, 25, entertained an offer from Washington but had said all along he wanted to return to Dallas.
The Cowboys restructured the deals of running back Ezekiel Elliott and right tackle La'el Collins earlier in the day to help with the new deal for Cooper and potentially to make room for a long-term contract for Prescott, Field Yates of ESPN reports.
Cooper spent much of 2019 on the injury report, with injuries to a foot, a quadriceps, an ankle and a knee. He played in every game, making 79 catches for 1,189 yards and eight touchdowns.
In 25 games with the Cowboys after a trade from the Raiders, Cooper has 132 catches for 1,914 yards and 14 touchdowns.