Born on August 7, 1925, in Aviles, Spain, Orbón lived in Cuba from 1940 to 1960, following which he moved to Mexico. In 1935, he studied at the National Conservatory of Oviedo in Spain. He then moved to Havana and began composing at an early age under the direction of Jose Ardevol. He was a member of the Grupo de Renovacion Musical during 1942-1949. In 1946, Orbón was awarded a grant to study at the Tanglewood Music Center with Aaron Copland. From 1946-1960, he was the director of the Orbón Conservatory, Havana, which was founded by his father, Benjamin. In 1954, he won the Juan de Landaeta Prize at the International Festival of Caracas (Venezuela) for his work. Tres versiones sinfónicas followed in 1958, along with one of his most important compositions, Concerto grosso for string quartet and orchestra. In 1955, the Fromm Foundation commissioned a work which was given its premiere in the Tanglewood Festival by a chamber group from the Boston Symphony Orchestra. In 1958, he received a scholarship from the John Simon Guggenheim Foundation; during that same year, he was given a commission to write a symphonic work by the Serge Koussevitzki Music Foundation. The original manuscript now constitutes part of the 20th century music collection of the Library of Congress in Washington

In 1959, George Balanchine selected Orbón to choreograph his Symphonic Dances as part of the Ballet Panamerica, which consisted of an evening of music from the more prominent composers of Latin America. In 1963, his Concerto Grosso was selected to represent Latin American music in the Baden-Baden Festival in Germany. He also collaborated with Pete Seeger on the musical adaptation of the famous Guantanamera tune and adapted the lyrics of the song based on a poem by Cuban poet, José Martí. He later became a lecturer at the University of Washington, the University of Miami, and at Princeton University. Orbón has given several lectures at institutions such as the University of Havana, Barnard College, the Spanish Institute of Columbia University in New York City, the Conservatory of Music in Mexico City, Washington University in St. Louis, and Rutgers University. He has also published important articles in both American and European artistic, literary, and musical magazines and journals.