He signed with Washington following a recent tryout.
Madison was a starter at strong safety for UT in 2013, making 41 tackles and registering 2.0 tackles for loss.
He joins five former Rocket teammates who also inked deals with NFL teams. Running back David Fluellen (Philadelphia Eagles), wide receiver Bernard Reedy (Atlanta Falcons), defensive end Jayrone Elliott (Green Bay Packers), quarterback Terrance Owens (Pittsburgh Steelers) and center Zac Kerin (Minnesota Vikings) all signed deals last week.