Gomez is the son of former Cuban Army Major Clemente Ricardo Gomez-Sicre (1906–1983) and Maria del Carmen Rodriguez-Fontanills (1915–1943).
He and his first wife, Gladys Brito-Izquerdo (1941- ) had three children, Dr. Maria del Carmen (1962- ), Dr. Elisa Alina (1963- ) and Clemente Romualdo Gomez-Brito (1967- ).
Gomez' sister, Isolina Elisa (1942- ), is married to Cuban diplomat Dr. Alfonso Fraga-Perez, and still lives in Havana, Cuba.
Gomez is the grandson of the Brigadier General Clemente Romualdo Gomez-Diaz, who served in the Cuban Independence War as chief of North Brigade of the Province of Matanzas.
He is the nephew of José Gómez-Sicre, who aside from working as a lawyer was also a noted art critic and author and Principal and founder of the Visual Arts Department at the Pan American Union in Washington, D.C. Gomez has other close relatives that has also contributed to the arts in Cuba; his great-granduncle Antonio Rodríguez Ferrer authored the musical introductory notes to the Cuban national anthem, while his cousin, sculptor Juan José Sicre created the most famous sculpture of José Martí y Pérez, located at Havana's Plaza de la Revolución.