Born in Dorset on 15 September 1986, Wilson took up shooting at his father's suggestion after he suffered nerve damage to his shoulder in a snowboarding accident which left him unable to play squash and cricket. He was raised on his parents' farm.
Wilson tried his hand at both skeet and trap but was not enthusiastic enough to train religiously for them. However, after trying double trap he found a discipline that he is happy to train for every day. Wilson was encouraged by Ian Coley after meeting at the Bisley shooting ground. Soon after this he was training with shooters such as Richard Faulds and Stevan Walton. Within four months of trying shooting at the Bisley Ranges, Wilson became the 2006 European Junior Champion at the tournament in Slovenia. In 2008 he attended the 2008 Summer Olympics as part of Great Britain's Olympic Ambition Programme to expose possible future Olympians to the Olympic experience. He began being coached by Ahmad Mohammad Hasher Al Maktoum, who is a member of the ruling family of Dubai and the 2004 Summer Olympics gold medallist in the double trap. Following budget cuts by UK Sport following the lack of shooting medals at the 2008 Summer Olympics, Wilson's funding was removed completely and he was required to fund his shooting expenses which amount to nearly £10,000 a year. He tried to work in a pub as a barman, but found that the night shifts conflicted with his shooting practice. His parents instead funded him for a year while he tried to secure further funding. He has also raised funds, along with the rest of the British shooting team, by running fundraising events. Wilson finished in fourth place at the 2011 European Shooting Championships in Belgrade with a score of 191 in the final. However, the British team came second overall, earning Wilson a silver medal alongside Stevan Walton and Richard Faulds. At a World Cup event held in Tucson, Arizona in 2012, Wilson set a new world record for the double trap. He scored 198 out of a possible 200 in the final, beating the previous record of 196. By winning a silver at the World Cup event in Chile in March 2012, he gained another quota spot for the British team for the 2012 Summer Olympics. He is a member of the Southern Counties shooting club. Having warmed up at the Royal Artillery Barracks in Woolwich in April in the test event for the Olympic venue, on 28 May, Wilson was named part of the British team at the 2012 Summer Olympics. He won gold, scoring 188 out of a possible 200 hits on 2 August 2012. It was Britain's first Olympic shooting medal since teammate Richard Faulds won the event in the 2000 Sydney Olympics. Wilson was appointed Member of the Order of the British Empire in the 2013 New Year Honours for services to shooting. On 31 October 2014, at the age of 28, Wilson officially announced his retirement from competitive shooting to focus on personal life and coaching, ending abruptly his short, but remarkable career with an Olympic gold medal in men's double trap from London 2012, and three more from the 2013 ISSF World Cup series.