After graduation from high school, he decided to attend University of North Carolina at Chapel Hill to play baseball.
After his junior season, he was selected by the St. Louis Cardinals in the 2006 Major League Baseball draft's 46th round.
The all-time winningest pitcher in program history at UNC, Woodard posted a career record of 34–5 over four seasons as a Tar Heel.
He was a three-time All-ACC performer and the 2006-07 recipient of the Patterson Medal, North Carolina's highest athletic honor.
He also left North Carolina ranking among the top 10 in Atlantic Coast Conference history in victories and innings pitched.