Gregory is the highest Dallas pick to sign so far. The four-year rookie deal was announced Wednesday.
The 6-foot-6, 245-pound Gregory will have a chance to start as a rookie with free agent defensive end Greg Hardy suspended for the first 10 games because of his role in a domestic violence case.
Some draft analysts had Gregory going in the top 10 before he tested positive for marijuana at the combine in February. He also missed one pre-draft meeting with a team and canceled two others.
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