Gurbux Singh started his athletic career as a badminton player, but soon took up field hockey as his sport of choice. He began to gain prominence as a university-level player, and also joined the Calcutta Customs Club in 1957, remaining there through 1965. He made his international début for India in 1961 and won gold medals at the 1964 Tokyo Olympics, as well as at the 1966 Asian Games.
Singh eventually switched to the Mohun Bagan field hockey team, where he would remain until his retirement. He had one more edition of the Olympics in him, however, and captured bronze in the tournament at the 1968 Mexico City Games as co-captain with Prithipal Singh. He then took up coaching and was the head of the French team in 1974-75, as well as the Indian team when they placed seventh at the 1976 Montreal Olympics. In 1981, he became an international umpire, and he also served several periods as a national selector. His brother Balbir was also a player on the 1968 Mexico City squad, as well as the 1966 Asian Games championship team.