The Steelers chose Spence with the 86th overall pick.
Spence will give Pittsburgh some depth at inside linebacker following the release of veteran James Farrior. Spence will compete with Stevenson Sylvester for a backup spot behind Lawrence Timmons and Larry Foote.
The 5-foot-11, 231-pound Spence started 40 games during his career with the Hurricanes and ranks 11th in school history with 318 tackles, including a team-high 106 tackles as a senior last fall.
Linebackers coach Keith Butler says he sees Spence eventually working behind Timmons and is impressed with Spence's speed, which should be a plus on special teams.