Green was one of the NFL's speediest and most skilled cornerbacks for two decades with the Washington Redskins. He was a seven-time Pro Bowler and a member of the 1990s All-Decade team.
The other player in his first year of eligibility, receiver Cris Carter, was not elected.
Monk, another long-time Redskin, finally was chosen in his eighth year of eligibility.
Inductions will take place at the Pro Football Hall of Game in Canton, Ohio, on Aug. 2.
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