Ozougwu was selected by the Houston Texans with the 254th and final pick of the seven-round draft.
The pick wrapped up three days of drafting by NFL teams at Radio City Music Hall in New York, which was conducted under the shadow of a renewed lockout of players by team owners.
The title "Mr. Irrelevant" was coined by former NFL receiver Paul Salata in the 1970s when he instituted a one-week vacation trip in Newport Beach, Calif., in honor of the last player taken in the draft, during which he is treated to golf tournament, a regatta and a roast.
Saturday began with the Carolina Panthers choosing Brandon Hogan, a 5-foot-10 defensive back out of West Virginia. Nebraska running back Roy Helu was taken by the Washington Redskins a few picks later in the fifth round.
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