Gaze led the senior Australian national team, the Boomers, to five Summer Olympic Games – including as the flag bearer at the opening ceremony of the 2000 Sydney Olympics, and he was also the Australian Team Captain. He was inducted into the Australian Basketball Hall of Fame in 2004, and the Sport Australia Hall of Fame in 2005, after being appointed a Member of the Order of Australia in 2002. In 2013, he joined his father, Lindsay, in the FIBA Hall of Fame, after being elected as a player, to become just the third Australian inductee. Two Australian basketball awards have been named in Gaze's honour: the NBL MVP award is named the Andrew Gaze Trophy, and the Australian International Player of the Year award is named the Gaze Medal.