McVeigh began his career at Tottenham, where he played 3 times before moving to Norwich City on a free transfer. Whilst at Norwich, McVeigh helped the club win promotion to the Premier League in 2004, and was a regular in the side during their Premier League campaign in 2004-2005. In a second spell at the club, McVeigh won the Football League Trophy in 2009, and was part of the squad that won the League One Title.

He was capped 20 times for his country, scoring four goals.