Gómez took up triathlon at the age of 15 after previously playing football and competing in swimming. However his career suffered a setback in 2000 when a routine medical test by the Consejo Superior de Deportes (CSD) revealed an "abnormal heart valve", leading to a six-year battle between Gómez and the Spanish sporting authorities regarding his right to compete internationally. He initially won this right in November 2003, but he was not selected for the 2004 Summer Olympics and in 2005 the CSD banned him from international and domestic competition until February 2006.
In the nine years from 2002 to 2010, Gómez took part in 57 ITU competitions and achieved 54 top ten positions, among which are 23 first place finishes. In 2003 and in 2008, Gómez was ITU Triathlon World Champion (both under-23 and Elite categories respectively in 2003). In 2007 and 2009 he was the Elite European Champion. He finished second in the World Championships in 2007 and was the runner up in 2011 ITU Sprint Distance Triathlon World Championships.
At the 2008 Summer Olympics in men's triathlon Gómez was among the pre-race favourites to win. With 300 meters to go in that race, Jan Frodeno was the leader of a group made up of Gómez, Athens 2004 Silver medalist Bevan Docherty of New Zealand, and Sydney 2000 Gold medalist Simon Whitfield of Canada. Whitfield opened up the gap with a sprint with only Frodeno responding. Frodeno sprinted away with 50 meters from the finish to claim the gold medal. Simon Whitfield took the silver medal five seconds behind, and New Zealand's Bevan Docherty won the bronze medal 12 seconds back. Gómez placed 4th, 20.64 seconds behind Frodeno.
In May 2013, Gómez competed in his first middle distance race by taking Gold in Challenge Half Barcelona. In February 2014 he raced and won his second middle distance race, Ironman 70.3 Panama.
In 2014, Gomez won his fourth ITU World Championships, winning four out of the eight possible races as well as placing third at the Grand Final, tying him for all time championships with Simon Lessing. Gomez also won the 2014 Ironman 70.3 World Championship.
In 2015 Gomez took his third consecutive ITU World Championship, and his fifth title overall, by finishing second at the Triathlon World Series Grand Final in Chicago.