The Seahawks announced the signings on Monday. Seattle also signed linebacker Mike Taylor and defensive back Terrance Parks.
Beckum, a third-round pick in 2009, caught 26 passes for 244 yards and three touchdowns in 48 games for the Giants from 2009-12. Taylor, who was undrafted in 2013, briefly spent time on Seattle's practice squad in December before being released. Parks played briefly for Hamilton in the Canadian Football League during the 2013 season after spending 2012 with the Kansas City Chiefs.