Murphy was Washington's first pick, the 47th overall. He led the nation last season with 15 sacks.
The 6-foot-5, 250-pound Murphy had 32 1/2 sacks over four seasons in college. He joins a roster that already is strong at his position thanks to two recent first-round picks who have been to the Pro Bowl, Brian Orakpo and Ryan Kerrigan.
The Redskins also announced Friday they added free-agent receiver Rashad Ross and waived receiver Kofi Hughes. Ross spent parts of last season on practice squads with the Titans and Chiefs.