Quinn, who sat out the 2010 season after being ruled ineligible by the NCAA for receiving improper benefits, was a first-team All-ACC selection in 2009. His 19.0 tackles for loss as a sophomore ranked first in the conference, and his 11.0 sacks ranked second.
"He's a great kid ..." Rams coach Steve Spagnuolo said. "We were very, very fortunate that he was there (at No. 14). ... When he's ready, he'll be thrown in there. I'm anxious to see him grow as a football player."
Quinn is UNC's 19th first-round pick in program history and the highest selection since the 2002 draft.
"We certainly spent a lot of time evaluating Robert Quinn," Rams general manager Billy Devaney said. "As we got closer to the draft we thought it'd be great if he was there. We didn't think there was much of a chance that he'd be there at 14. ... The grade we had on Quinn was significantly higher than the other (available) players in the pool. It ended up being a really easy decision. ... He just seems like a real good fit, so we're thrilled to have him."
Quinn is the 31st first-round selection coached or recruited by Butch Davis in 10 years as a college head coach.
"The best thing he does is come off the edge. He has great acceleration, great burst, great first-step explosion. He's relentless in chasing the passer," Butch Davis said on the NFL Network. "He's an awful lot like (former New York Giant) Michael Strahan."
(UNC Athletic Communications contributed to this report)