A former pupil of Harris Academy, Addison was briefly attached to Hibernian aged 16 before returning to his native Tayside. After a season playing with Junior side Lochee United he signed for Jim McLean's Dundee United.
Considered part of the club's move towards home-grown players, he broke into the first team at the same time as John Holt and Ray Stewart and Billy Kirkwood. However, he was unable to establish himself as a regular in the side: in his eight seasons at Tannadice he only once made more than twenty league starts.