The defensive tackle had been expected to be one of the first players chosen from this year's draft class, but the 21-year-old was still available when the Vikings prepared to make their first of three picks in the first round.
General manager Rick Spielman told reporters: "I went through a thousand scenarios at that 23rd and 25th pick and I can tell you honestly he was not in one of those scenarios.
"So for him to fall down to our lap, there were some conversations as he fell to potentially even move up. But as the names kept falling off the board, we had more than enough options to just sit there and let everything fall to us. And when Sharrif fell to us, it was something that was very unexpected."