General manager Mickey Loomis, who announced the move Tuesday, says the Saints also have signed their third-round choice, cornerback P.J. Williams. Both players have agreed to four-year contracts.
Stanford offensive tackle Andrus Peat, drafted 13th overall, remains the only unsigned draft pick on New Orleans' roster.
The 6-foot-3, 245-pound Anthony, picked 31st overall, led Clemson with 90 tackles last season. He was credited with 10 1/2 tackles for losses, 2 1/2 sacks, two forced fumbles and an interception.
The 6-foot, 196-pound Williams, who was the second of two third-round picks, had four career interceptions at Florida State.
The Saints open a three-day rookie camp on Friday.
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