Contract terms weren't immediately available. Pryor visited the Jets this week, along with the Seattle Seahawks.
News of the deal was first reported by Newsday.
Pryor's arrival gives the Jets four proven veterans at receiver, led by returning starters Robby Anderson and Jermaine Kearse. They also have Quincy Enunwa, who is coming back from a neck injury that caused him to miss the season.
With Pryor on board, the Jets could look to move on from Anderson or Kearse. Anderson is coming off a breakout season, but off-the-field issues (two arrests since last May) are a concern for the organization. Kearse was solid in his first season with the Jets, but he's due to make a non-guaranteed $5 million in 2018.
Pryor, 28, signed a one-year deal with Washington last offseason, rejecting a multiyear offer by the Cleveland Browns after a breakout season in 2016. But the move didn't work out for Pryor, who started at the X position but finished with only 20 catches for 240 yards and 1 touchdown in nine games.
He injured his ankle in a Week 2 win at the Los Angeles Rams, and he eventually needed season-ending surgery in November.
Pryor was not the focal point of Washington's offense the way he was in Cleveland. In his first full season as a receiver, Pryor caught 77 passes for 1,007 yards and four touchdowns. He had switched from quarterback to receiver in the 2015 offseason but played in only three games that season.
In 2011, the Oakland Raiders picked Pryor in the third round of the supplemental draft. He started 10 games at quarterback while appearing in five others over three seasons.
ESPN's John Keim contributed to this report.