McGee became the first Hurricane taken by the Rams since they drafted defensive tackle Damione Lewis in the first round of the 2011 draft.
McGee, whose selection means the Hurricanes have now had at least one player drafted for 39 straight years, was a two-year starter for the Hurricanes.
After playing mostly quarterback at Plantation High, McGee became a four-star defensive back recruit because of his size, speed, and playmaking ability in the secondary.
A starter over the final 24 games of his college career, McGee finished his senior season with 54 tackles and two interceptions. He also broke up a team-best seven passes while emerging as the team's top cover guy in 2012.
McGee graduated from the University of Miami in December.