"This is truly an honor," Curtis said from his home. "I'm excited about the opportunity to continue playing football on the professional level and look forward to the challenge.
"I've been looking forward to this day for a long time, but I'm glad the call finally came and I can move on to the next phase of my career."
Curtis finished his career second on the all-time tackles list with 422 and ranks among the top 10 at Tech with 10 career interceptions, including a season-high four in 2001.
His star began to shine following his sophomore season, when he logged a single-season best 153 tackles to earn All-Big 12 and All-America honors. Curtis also earned All-America accolades each of the last two seasons, including second-team All-America honors as a senior.
Curtis' draft position is the highest for a Tech player since the 1999 draft when Denver selected defensive end Montae Reagor in the second round.
In the 2000 draft, Anthony Malbrough and Sammy Morris both were drafted in the fifth round. Kris Kocurek was a seventh-round pick for Seattle last year.