The Vikings picked Cook with the 34th overall selection on Friday.
The Vikings acquired the pick the day before by trading their first-rounder, No. 30 overall, to Detroit. The Vikings and Lions also swapped fourth-rounders, and Detroit sent Minnesota a seventh-round selection as part of the deal.
Vikings officials liked enough of the early second-round prospects to move down and wait for the second day of the draft to select their first player.
Cook has good size for his position at 6-foot-2 and 212 pounds. His career at Virginia was hindered by injuries and academic problems, but he had a strong senior season, leading the Cavaliers with four interceptions.