Gil-Ordóñez was born in Madrid on September 5, 1957. He loved film scores as a child and sang in his school choir, later taking lessons on violin, guitar, and accordion, and when he was 12 he was attending symphonic concerts with family friends. Gil-Ordóñez's family, however, insisted he study engineering at the Polytechnic University of Madrid before committing to a musical career. He completed his engineering degree as agreed then turned to music, studying composition, violin, and conducting at the Conservatorio Superior de Música. He moved on to study composition with Pierre Boulez and Iannis Xenakis in Paris, but his career choice was set when he heard Sergiu Celibidache conduct the London Symphony Orchestra in 1978. He moved to Munich in 1985 to study with Celibidache and took conducting courses at the Scuola di Alto Perfezionamiento Musicale in Saluzzo, Italy. He also continued to study composition. Gil-Ordóñez conducted major Spanish orchestras and was appointed associate conductor of the National Symphony Orchestra of Spain in 1991. He continued to work in Spain, conducting the Valencia Symphony Orchestra in the Spanish premiere of Leonard Bernstein's Mass in 2000.
In 1994, he moved to the U.S., settling in Washington, D.C. He founded two new organizations in 1997 that allowed him to explore his interests in contemporary music: the ensemble Musica Aperta in Washington, and the agency IberArtists New York. He remains music director of the latter group, which aims to promote Spanish music and artists in the U.S. At IberArtists, he came into contact with the consultant and musicologist Joseph Horowitz, who was also interested in Spanish music. The pair co-founded the Washington ensemble PostClassical, which has been acclaimed for its innovative programming. Gil-Ordóñez continues to serve as the group's music director and conductor. He is also principal guest conductor of the Perspectives Ensemble in New York and has guest conducted several major American orchestras. Gil-Ordóñez is an advisor to the Trinitate Philharmonia in León, Mexico, a group that has tried to replicate the success of Venezuela's El Sistema.
Beginning with a 2007 PostClassical recording of Virgil Thomson's The Plow That Broke the Plains, Gil-Ordóñez has recorded mostly contemporary music for the Naxos label, also with the Perspectives Ensemble. With that group he released a new recording of the original version of Falla's El amor brujo in 2019. In 2006 the king of Spain inducted Gil-Ordóñez into the Royal Order of Queen Isabella, the country's highest civilian honor.