Knighton, a team captain for the Denver Broncos this past season, was a two-year starter after signing in free agency in 2013.
He proved to be a durable -- he started 16 games in back-to-back seasons -- and productive player in the middle of the defense.
Knighton completes a defensive line for Washington that has been overhauled out of necessity.
The Redskins wanted Jarvis Jenkins to use his athleticism to rush the passer; it never happened.
So they replaced him with someone who can do that in Stephen Paea, who can also move inside on nickel downs.
That's what they'll ask Jason Hatcher to do as well -- if Hatcher stays healthy.
Knighton, 28, played largely in the base defense for the Broncos -- he had 31 tackles in 2013, 30 tackles in '14 -- but routinely gobbled up double teams and kept the Broncos linebackers free to run to the play.
Had he stayed with the Broncos he would have been a fit at nose tackle in the team's 3-4 look with Wade Phillips as the defensive coordinator.
Knighton's departure will move Sylvester Williams, the Broncos' first-round pick in the 2013 draft, into a more prominent role.
ESPN.com's John Keim and Jeff Legwold contributed to this report.