Aiden McVeigh was spotted by Sammy Morgan playing in his native Northern Ireland. He came to Carrow Road on trial in September 1999 playing in a 4-0 defeat to Aston Villa in a FA Premier Academy match. The Football Transfers Website linked Aiden with a move from Glenavon to Scottish side Ayr United and on 29th May, Aiden completed the move across to Scotland.

However Aiden has been homesick for nearly all his time in Scotland and spent some of the 2002/03 season on loan to Northern Ireland side Ards. This was disappointing as he made just 7 appearances - only one of which was not from the substitute's bench. He also had a loan spell with Scottish non-leaguers Cumnock Juniots which was slightly more successful.

In May 2003, Aiden was released by Ayr. He joined Northern irish side Glenavon before transferring to Dungannon Swifts for the 2006/7 season.