Glenn, who played at Kamiak High School, was one of six players who attended the Chiefs' rookie minicamp last weeked who were signed by Kansas City.
The 5-11, 214-pound Glenn played in 40 games in four years at Washington, starting 16. He had 152 tackles (93 solo), three tackles for loss, four fumble recoveries, three interceptions and four passes defensed.
Glenn was honorable-mention All-Pac-12 in 2012 and was named the Most Outstanding Special Teams Player at the team’s postseason awards banquet.
The Chiefs also signed running back Jordan Roberts, defensive linemen Risean Brousard and Miguel Chavis and defensive backs Greg Castillo and James Rogers after the team's rookie minicamp.
The Chiefs released fullbacks Ryan D’Imperio and Nate Eachus and safety Jose Gumbs.
Running back Knile Davis, selected by the Chiefs in the third round of the NFL Draft last month, also signed on Monday.
The Chiefs are hoping the 227-pound Davis can be a power back to complement the speed and big-play ability of Jamaal Charles. But they also believe Davis has the speed and ability to be more than just a goal-line and short-yardage alternative to Charles.
Davis had a huge season at Arkansas in 2010, rushing for 1,322 yards and 13 touchdowns. But he missed all of 2011 because of a broken ankle.
Last season Davis fumbled numerous times and missed a couple of games because of a hamstring injury. He rushed for only 377 yards.
The Chiefs have now signed three of their eight draft picks. They previously signed sixth-round center Eric Kush and seventh-round linebacker Mike Catapano.
Unsigned are first-round tackle Eric Fisher, third-round tight end Travis Kelce, fourth-round linebacker Nico Johnson, fifth-round defensive back Sanders Commings and sixth-round fullback Braden Wilson.
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