Elliott was brought up in Rawmarsh, near Rotherham, South Yorkshire. He attended Rawmarsh Comprehensive School and later worked as a joiner at British Steel Corporation. Remarkably, he managed to establish himself as a world class athlete while working full-time. He began his athletic career by running in the Young Athletes League for his local club, Rotherham Harriers, and his 800m time of 1 minute 53.3 seconds has been the under-17 record since 1979. Elliott also held the UK under-17 record with a time of 1 minute 50.7 seconds, which stood for nearly 10 years. He excelled as a schoolboy athlete, winning four English Schools titles, twice at 800 metres and twice over the country. In August 1982, he set a 4 × 800 metres relayWorld Record of 7 minutes 3.89 seconds with fellow British Athletes Sebastian Coe, Steve Cram and Garry Cook. At the 1983 World Championships held in Helsinki, he finished 4th in the 800m final. Elliott was unfortunate to miss out on selection for the 1500m at the 1984 Olympic Games in Los Angeles, losing out to the eventual gold and silver medallists, Sebastian Coe and Steve Cram, and the world record holder at the time, Steve Ovett. At the time, it was a very controversial decision. Ovett and Cram had already secured their places. The third place was either Coe's or Elliott's. Although Elliott defeated Coe at the AAA's Championships which somehow came to be viewed as a "race off" between the two, the selectors opted for Coe. Elliott was selected for the 800m and qualified for the semi-finals, but had to withdraw due to an injury. Elliott won a bronze medal in the 800m at the 1986 Commonwealth Games in Edinburgh behind Steve Cram and Tom McKean. He then won a silver medal in the event at the 1987 World Championships in Rome. The following year, he won the silver medal in the 1500m at the Olympic Games in Seoul. He also finished fourth in the Olympic 800m final. In January 1990, he became the Commonwealth champion over 1500m in Auckland. Later in the year, Elliott ran an outstanding 1:42.97 over 800m in Seville. This made him the favourite to win both middle distance gold medals at the 1990 European Championships in Split. However, due to injury problems he only entered for the 1500m and was tripped in the semi-final. After an appeal by the British team he was reinstated, and went on to finish fourth in the final. A year later, Elliott had his revenge when he defeated the European champion Jens-Peter Herold in the 1500m race at the European Cup in Frankfurt. He also won the Fifth Avenue Mile in 1987, 1989 and 1990, the latter in 3:47.83 min. After retiring from competition running in 1992, Elliott became a coach and race organiser. He joined Newcastle-based sports marketing agency Nova International, where he was Director of Running. In 2004 he became the Athlete Services Manager for Yorkshire at the English Institute of Sport in Sheffield.