From 2005 to 2009, Wright was head coach at the Melbourne University Boat Club. Wright worked for Rowing New Zealand as coach for the men's eight, and was head coach at the Waikato Regional Performance Centre with training at Lake Karapiro. In late 2014, Wright was appointed head national coach of Switzerland. He led the lightweight men's four to become the 2015 world champions. A year later, the same boat won Olympic gold at the Rio Olympics. In September 2016, he was appointed head rowing coach for Australia's men. Within a year of Wright starting in Australia, the Australian men's four—consisting of Joshua Hicks, Spencer Turrin, Jack Hargreaves and Alexander Hill—won gold at the 2017 World Rowing Championships in Sarasota, Florida. Until 2017, Australia had not won a World Championship in the Men's Coxless Four since 1991 in Vienna, Austria.