Johnson was released by the Bengals on Sunday, Adam Schefter of ESPN reports.
The veteran of 14 NFL teams signed with Cincinnati in March to compete for a backup role behind Joe Burrow, but he found himself the odd man out next to fellow veteran signing Joe Flacco and developmental prospect Sean Clifford. Johnson saw action in five regular-season games and on 137 offensive snaps for Washington last year, completing 63 percent of his passes for 372 yards, one touchdown and two interceptions.