Head coach Jay Gruden announced Friday that McCoy will start over Dwayne Haskins and Case Keenum.
Gruden told reporters Wednesday he wasn't ready to name a starter for Week 5 until he saw more from his quarterbacks.
"I have to see some things for me to make the decision, and that'll come out here at practice tomorrow," he said. "Hopefully, after tomorrow's practice I'll have a good indication of who I want to play. So, yeah, in my mind, I have a pretty good plan—contrary to belief."
Keenum started Washington's first four games, but he was removed in the second quarter last week against the New York Giants with a foot injury that had been bothering him heading into the matchup.
Haskins made his NFL debut in taking over for Keenum, and his inexperience showed. The former Ohio State star threw three interceptions in 17 pass attempts and finished with 107 yards.
Gruden has seemed hesitant to test Haskins. He told reporters in March that developing a young quarterback wasn't something that interested him: "There is no developmental process here. This is not Triple-A baseball, we're not trying to develop a pitcher here. We're trying to win a game right now."
Les Carpenter of the Washington Post reported Friday that Gruden "did not want" Haskins when the team drafted him No. 15 overall.
McCoy will take the reins of Washington's offense against a Patriots defense that has allowed the fewest points per game in the NFL (6.8). He hasn't played since fracturing his right fibula in Week 13 last season against the Philadelphia Eagles.