The Patriots selected him 17th overall in the first round of the 1999 draft. Woody would go on to start 76 games with the Patriots, mostly at center.
Woody was known to struggle with delivering the snap in the shotgun formation. When a play was called that required a shotgun snap to the quarterback, Woody would rotate to the guard position.
As the anchor of a tough and effective New England offensive line, Woody was a member of two Super-Bowl-winning teams, in 2001 and 2003. He did not play in Super Bowl XXXVIII against the Carolina Panthers because of a knee injury.
Woody signed as a free agent with the Detroit Lions in March 2004 and started every game in the 2004 and 2005 seasons before missing most of 2006 on injured reserve. His play earned him a selection as a Pro Bowl alternate in 2004.
On March 2, 2008, Woody and the Jets agreed to a five-year, $25 million contract with $11 million in guaranteed money.
During the Jets' post-season run, Woody suffered a torn Achilles tendon in a victory over the Indianapolis Colts on January 8, 2011. Woody was subsequently placed on the injured reserve list on January 12, 2011. Following the injury, Woody was released by the Jets on February 28, 2011.
Woody announced his retirement on July 26, 2011.