He joined Norwich from Peterborough in December 2003 for a fee of £325,000, and instantly won over the Canaries supporters by scoring twice on his debut to help beat local rivals Ipswich Town at Portman Road and go top of the First Division. His goals made a significant contribution to Norwich's promotion to the Premier League as First Division champions at the end of the 2003–04 season. Within a year, he had turned from a Second Division to a Premiership player. McKenzie took time to find his feet in the Premiership but he established a strike partnership with Dean Ashton which would become one of the most potent in the division during the closing stages of the 2004–05 season. His goals helped Norwich to haul themselves into contention to avoid the drop, although they were relegated on the last day of the season.