Northern Ireland striker Paul McVeigh spent 3 days on trial at Norwich in mid March 2000 following the announcement by Tottenham that he was surplus to requirements. Familiarity with fellow Irishmen Bryan Hamilton and Adrian Coote may have influenced the decision for him to head to Colney. Paul had spent a period on loan with Cambridge earlier in 1999/2000. Hamilton described Paul as "a good young player , very bright; I like pacy and energetic players. He's come in to spend a few days with us, we'll take it as it comes before we make any decisions on him." With Des Hamilton and Garry Brady occupying the 2 loan spots, Bryan Hamilton moved to sign Paul on a contract until the end of the 2000/2001 season.

Paul had a good game in his debut for the Reserves against Brighton despite the 2-1 defeat. He had two good opportunities one of which was disallowed.

Paul was impressive for the reserves during 2000/01 scoring eighteen goals but never made much of the few opportunities he had in the first team. 2001/02 was a different situation. Replacing the injured Chris Llewellyn, Paul made himself a regular in the first team, scoring and setting up vital goals. As a reward, Paul was called up to the Northern Ireland squad for the World Cup qualifiers against Denmark and Iceland in September 2001.

His impressive form at the beginning of the 2001/02 season led to an extension to Paul's contract that sees him tied to Carrow Road until 2004. His form continued throughout the 2001/02 season with 10 goals in 48 appearances. 2002/03 started well with 4 goals in the first 4 league games (2 goals in the 4-0 thrashing of Grimsby, 1 goal in the 2-0 win at Brighton and the winner in the defeat of league leaders Gillingham). This brought the attention of Premiership side Charlton who were rumoured, according to The Evening Standard to be preparing a £750000 bid for Paul's services. In March 2003, the Football Rumours website suggested that Tottenham would attemp to re-sign Paul as manager Glenn Hoddle felt it was a mistake to have let him go. Paul finished the 2002/03 season as City's top scorer netting 15 goals in 41 appearances.

Paul signed a new two and a half year contract with Norwich on 12th January 2003.

Reports in the People on 27th March 2005 suggested that Paul will depart Carrow Road in the summer of 2005. This became more likely when Paul was transfer-listed at the beginning of May 2005. The People then reported on 3rd July 2005 that Sheffield Wednesday were keen to sign him. However he was taken off the transfer-list in mid-July 2005 with Worthington impressed by his commitment to pre-season training and to rectify the other losses to Norwich's squad

Paul was linked with a switch to Harry Redknapp's Portsmouth at the end of December 2006 according to reports on the Football Rumours website. The following month saw him linked with switches to both Brentford and Nottingham Forest.

On 22nd March 2007, Paul was loaned to Burnley until the end of the 2006/7 season as he was out of manager Peter Grant's plans - having made just 6 starts during the 2006/7 season. He was linked at the end of March 2007 with a move to Charlton. Paul was indeed released by Norwich at the end of the 2006/7 season.

At the end of July 2007, Paul trained with Italian Serie B side Pisa and Norwich's Championship rivals Plymouth Argyle. "We will be having a look at Paul McVeigh, who is currently out of contract,” said Pilgrims boss Ian Holloway. “Not having Kevin Gallen, I would like to have a look at someone else. I might need someone on that right-hand side, who can do a dual role if we get some injuries.” Paul signed a two year deal with Luton Town on 10th August 2007. Unfortunately McVeigh couldn't help Luton avoid relegation to League Two in 2007/8. Following relegation, Paul was released by the Hatters.