That leaves only one unsigned player for the Giants from this month's selections, defensive tackle Jay Bromley, taken in the third round.
In addition to Beckham, a wide receiver drafted 12th overall, center Weston Richburg (second round), linebacker Devon Kennard (fifth round) and cornerback Bennett Jackson (sixth round) signed with the team Monday.
Beckham joins another LSU receiver, Rueben Randle, in New York's passing attack, which lost veteran Hakeem Nicks in free agency. Beckham set an LSU record with 2,315 all-purpose yards in 2013, completing his career with 15 touchdowns and 4,118 all-purpose yards, which ranks No. 5 in school history.
''He has great speed. He's polished. He has great hands and played at the top level.'' Giants coach Tom Coughlin said when the team drafted Beckham. ''He's someone we could count on putting the ball in the end zone and we can also feature him in the kicking game as well.''
Richburg was a four-year starter at Colorado State who made 50 consecutive starts, a school record. He was first-team All-Mountain West in 2013.
On Friday, the Giants signed fourth-round running back Andre Williams and fifth-round safety Nat Berhe.
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