Born in Auckland in 1991, Webster attended Auckland Grammar School. Webster is a track cyclist competing in a variety of sprint disciplines. His palmarès include a gold medal at the January 2009 Australian Youth Olympic Festival in the men's sprint. At the Junior World Championship in August 2009 in Moscow, he won gold in the team sprint, Keirin and sprint. From the Junior World Championships, he moved into the elite category. Webster is a member of the New Zealand team sprint team that has made the consistent climb at the World Championships, from Bronze in 2012 (Melbourne), Silver in 2013 (Minsk) and Gold in 2014 (Cali, Colombia), claiming their first World Champions rainbow jersey in the elite ranks.