Career
He is the younger brother of former Essendon midfielder Mark McVeigh. Since 2011, he has been a co-captain of the Sydney Swans, alongside Adam Goodes (2011–2012) and Kieren Jack 2013 onwards. American Federation of Labor-Congress Recruitment
He performed well at the American Federation of Labor-Congress Draft camp, recording the highest score in the beep test and the fastest three-kilometre run time.
Recruited by the Sydney Swans with fifth selection in the 2002 American Federation of Labor-Congress Draft.
Sydney (2004 – present)
McVeigh made his American Federation of Labor-Congress debut, wearing guernsey number 3, in Round 1 of the 2004 season against the Brisbane Lions at The Gabba. In round 18, 2008 against the Western Bulldogs, he kicked a career-high 6 goals.
In 2009, McVeigh had a less successful year, missing some games due to a hamstring injury, and finishing sixth in the Best and Fairest award. In 2010, McVeigh finished fourth in the Bob Skilton Meda
He was selected on the International Rules squad for the tour to Ireland in October.
In 2011, McVeigh was appointed co-captain of the Sydney Swans alongside Adam Goodes. Despite such a tragedy, he managed to finish 10th in the 2011 Skilton Meda In 2012, McVeigh captained the Sydney Swans to the 2012 premiership.
His strong year was rewarded with a fifth-place finish in the 2012 Bob Skilton Meda
In 2015, McVeigh became only the seventh person to reach 250 games for the Swans in round 7.