Ochoa was born in Cuba to a musical family. He trained at the Conservatorio Internacional de M‹sica in Havana and made his professional debut at 17 conducting Verdi's Il trovatore. He continued his conducting studies in Europe at the Real Conservatorio de Madrid, the Accademia di Santa Cecilia in Rome and in Vienna with Hermann Scherchen.
Upon his return to Havana, Ochoa founded the Sociedad Coral, which collaborated with the Vienna Boys' Choir during their Havana concerts, a relationship that led to the creation of the Niê±os Cantores de la Habana.
Ochoa was also professor of conducting at the Conservatorio Nacional de Cuba and led the Orquesta Filarmonica de la Habana. In Europe, he led the Orquesta y Coro de la Radio Nacional de Espaê±a, the Orquesta de Camara de Madrid and the Piccola Opera di Roma.
Ochoa founded the Miami Symphony Orchestra, which has a strong Hispanic profile, in 1989. Traditionally, the season opens with a performance starring guitarist Angel Romero, who is sometimes joined by other members of the Romero guitar family. Ochoa appointed Venezuelan conductor and composer Eduardo Marturet as associate principal conductor last season.
A biography on the orchestra's website quotes Ochoa as saying, "You need to have some of Don Quijote inside to create a symphony orchestra."
The cause of death was heart failure, according to the Herald.