Moore is best known for his two spells with Scottish Premier Division / Scottish Premier League club Rangers. Having graduated through their youth system, he made 252 appearances for the Glasgow based club from 1993 to 2005, punctuated with a season in England with Crystal Palace in the 1998–99 First Division. In his time at Rangers he became team captain and won numerous domestic league and cup honours, including making 44 appearances and scoring four goals in their 2002–03 Treble-winning season.
After leaving Rangers on a free transfer in January 2005, Moore spent a half-season at German Bundesliga club Borussia Mönchengladbach, before moving to English Premier League club Newcastle United. Released by Newcastle after an injury hit two seasons, Moore moved to his hometown club Queensland Roar (later renamed Brisbane Roar) in the Australian A-League, as their captain and Marquee player. After three seasons with the Roar, in January 2010 Moore moved to Greek Super League side AO Kavala, only to leave in March.
In international football, Moore has made over 50 appearances for the Australia national team, including at the 2006 and 2010 World Cups in Germany and South Africa. Having made his debut in 1995, he has been Australian team captain a number of times.