The team announced the deal Tuesday.
All 10 of Washington's draft choices are under contract.
Scherff, an offensive lineman from Iowa, was the No. 5 overall pick in the draft. The Redskins hadn't taken a player in the first round since 2012, when they chose Robert Griffin III after sending a bevy of picks to the St. Louis Rams to move up in the draft.
The 6-foot-5, 319-pound Scherff played left tackle in college, but the Redskins plan to move him to the right side of their line.
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