 Raised in Hamilton, Wright started his career with Aberdeen – progressing through the ranks alongside Eoin Jess and Scott Booth – and made nearly 150 league appearances for the "Dons"; he was part of the squad that came close to winning the League title on the final day of the Scottish Premier League in the 1990–91 season, and achieved further league runners-up finishes in 1993 and 1994, plus reaching finals in the 1992–93 League Cup and Scottish Cup.In 1995 they escaped relegation only via a playoff (his last matches for the club), an unexpected situation which meant Wright celebrated his wedding prior to the tie rather than after the season's conclusion as he had planned.In summer 1995 he joined his boyhood heroes (and Aberdeen's main rivals) Rangers for £1.5m.